When Affordable Care Act insurance marketplaces launched in fall 2013, Arizona seemed like a success. Eight insurers competed to sign up consumers, offering a wide variety of plans and some of the lowest premiums in the country.

Today, with ACA enrollment starting Nov. 1, Arizonans will find in most counties only one insurer selling exchange plans for 2017. Premiums for some plans will be more than double this year, some of the biggest increases in the nation. Only last-minute maneuvering prevented one Arizona county from becoming the first in the nation to have no exchange insurers at all.

A similar dynamic is playing out in other states’ exchanges, which are a critical centerpiece of the 2010 health law. About one-third of U.S. counties will have just one exchange insurer next year, up from 7% this year, estimates the nonprofit Kaiser Family Foundation, which studies health-care issues. In many cases, remaining insurers are seeking significant rate increases.

A look at what happened in Arizona shows problems with the design and implementation of the ACA, combined with early missteps by insurers. Some priced plans aggressively, angling for market share and betting special programs built into the law would protect them from losses. Those protections didn’t work as expected. Enrollees’ health-care expenses repeatedly overshot the projections of nearly all Arizona’s insurers. The result: a flood of red ink, then withdrawals and premium increases.

“The Arizona market is the poster child for the problems the exchanges are experiencing nationally,” says Tom Snook, a Phoenix-based actuary for consultants Milliman Inc.

Opponents of the health law have cited the problems in Arizona and other states to argue for unraveling the legislation, and they have proposed changes such as expanding health-savings accounts and allowing insurers to sell plans across state lines.

Affordable Care Premiums to Spike an Average 25% in 2017 WSJ's Stephanie Armour has analysis of the Affordable Care Act premium increase as well as the impact of insurers fleeing the program on Lunch Break with Tanya Rivero. Photo: AP

Obama administration officials say they are bolstering the exchanges, and the consumer impact of premium increases will be limited by the law’s subsidies for lower-income people, received by about 85% of enrollees nationally. “We’re making really good progress in addressing a lot of the issues,” says Kevin Counihan, head of the Centers for Medicare and Medicaid Services unit charged with implementing the health law. He calls Arizona an “outlier,” saying that insurers elsewhere have succeeded with ACA plans.

The ACA transformed the individual insurance market, where consumers buy their own plans. Before the law, insurers could refuse to sell to people with pre-existing health conditions. Starting in 2014, consumers couldn’t be denied coverage, or charged more, if they were ill. Individuals could shop for plans via an online marketplace. Partly to ensure that healthy people signed up to balance out the sick, the law contained penalties for most people if they didn’t obtain coverage. Arizona expanded Medicaid, as the law envisioned.

Insurers saw uncertainty in the new marketplace, but also potential. They had to guess what prices they needed to charge to cover the health costs of new enrollees. A 2013 Society of Actuaries report suggested that the Arizona individual-insurance market could more than double, growing to 570,681 consumers, with more than 80% of them buying through the exchange. The health-care costs of the newer customer base would be around 22% higher than the old one, it suggested.

Insurers believed they had protective guardrails—programs in the law to limit losses for companies that drew a lot of unhealthy, high-cost consumers. One insurer, Health Net Inc., told investors in November 2013 it could effectively pay out $1.20 in claims for each $1 it got in premiums and still break even with help from an ACA program called “risk corridors.” Some of Health Net’s Arizona products were among the lowest-priced in the country, according to Kaiser.

Kim Walton, 62 years old, of Tempe, says his monthly insurance bill dropped by more than two-thirds compared with his pre-ACA plan, with help from a federal subsidy. Unlike his old plan, his new ACA insurance covered any costs tied to his pre-existing health conditions—he earlier had a hip replacement and suffered a broken neck. “It was perfect,” says Mr. Walton, who owns his own business.

Krysti Horowitz of Phoenix says she and her husband decided to keep the insurance they already had, an option the Obama administration authorized in late 2013. Photo: Caitlin O'Hara for The Wall Street Journal

Krysti Horwitz of Phoenix steered clear of the exchange. Ms. Horwitz, 35, and her husband, who own an online-marketing business, were healthy. In 2013, they had a plan that she said cost them significantly less than a new ACA one would. They weren’t eligible for subsidies. They decided to keep what they had, an option the Obama administration authorized in late 2013.

By spring of 2014, with the first year of the new ACA plans barely under way, insurers had to guess again at pricing. Rate requests for 2015 plans were due, though insurers still had scant information about who signed up. That was partly because federal officials extended the deadline for enrollment after technical problems with HealthCare.gov, the federal exchange being used in Arizona and many other states.

One thing was already clear: Health Net’s low-price gambit had won huge market share. The company ended up with nearly 92,000 enrolled in individual plans in 2014, more than seven times its 2013 total, according to insurance-data firm Mark Farrah Associates’ Health Coverage Portal.

That posed a challenge for rivals, including startup Meritus, one of the nonprofit cooperative plans launched under the ACA. Meritus drew only a few thousand consumers in 2014, and it needed to boost enrollment to sustain itself, according to Tom Zumtobel, the co-op’s former CEO, who took over in late 2014.

Meritus worked to reduce its prices, and its rates came in below competitors’ in 2015.

Once again that year, Arizona had some of the lowest exchange premiums in the U.S., and one of the most competitive marketplaces, with 11 insurers, according to the Kaiser data. Enrollment grew, particularly at Meritus, where it surged to about 48,000 in 2015, according to Mark Farrah Associates.

On Oct. 1, 2015, insurers got a huge blow: Federal regulators announced the risk-corridor program, which many companies expected to limit their financial risk, would pay out only 12.6% of the amount expected. The program hadn’t taken in enough money from successful insurers to cover the requests of those with significant losses.

For Meritus, it was “operationally devastating,” says Mr. Zumtobel. That Oct. 30, just two days before consumers were set to start buying their 2016 exchange plans, Arizona’s regulator put the co-op under supervision, barring it from selling new insurance policies.

Remaining insurers began retrenching. The 2016 plans included more-limited networks of health-care providers. The total number of exchange insurers ticked down to eight, from 11, and premiums rose. “We started to see the cracks,” says Jerry Anderson, an insurance agent in Scottsdale, Ariz.

Blue Cross Blue Shield of Arizona decided to stop selling ACA-exchange plans in Maricopa County next year. Photo: Caitlin O'Hara for The Wall Street Journal

Nearly all the Arizona individual business of exchange insurers plunged into the red, according to Mark Farrah Associates, the insurance-data firm. Health Net booked nearly $40 million in losses on its Arizona individual business in 2014, and another $39 million the following year, according to Mark Farrah Associates, when the insurer agreed to be acquired by Centene Corp. Blue Cross Blue Shield of Arizona, the biggest player in the state’s individual market, had priced less aggressively than Health Net but still saw steep losses.

Based on regulatory filings, McKinsey & Co. estimated the insurance industry suffered cumulative losses of between 9% and 11% of premium revenue on individual plans last year. Only about one-quarter of insurers reported a profit on the business.

In Arizona, insurers set their rates too low to cover their enrollees’ health expenses. There were fewer people than actuaries once projected, with about 203,000 choosing exchange plans during the enrollment period for this year. The share of enrollees who were healthy was smaller than companies projected, partly because the law’s penalties weren’t enough to prod them to enroll, insurers say. The unhealthy people who did sign up were more costly. Insurers say that some consumers appeared to be buying plans specifically when they had health needs.

Blue Cross Blue Shield of Arizona’s ACA plans in 2014 were priced around 35% higher on average than its individual plans in 2013. “In hindsight, it wasn’t even close to enough,” says Jeff Stelnik, a senior vice president at the nonprofit. ACA-plan enrollees had medical costs around 250% higher on average than individual members before the health law, due partly to far higher prevalence of conditions such as diabetes, he says.

Insurers began to bail out. On April 19, UnitedHealth Group Inc. said it would pull out of nearly all state ACA exchanges, including Arizona’s, for the next year amid growing losses. Others in Arizona retreated, including Blue Cross Blue Shield of Arizona and Health Net, which decided to pull out of the state’s most populous county, Maricopa, as well as adjacent Pinal, for 2017. On Aug. 15, Aetna Inc. announced it would leave most of its exchanges, including Arizona’s.

Aetna’s decision created a crisis: Pinal County would have no exchange insurers for 2017. The void would short-circuit a central mechanism of the law, because consumers can get subsidies only through an ACA marketplace.

The situation drew attention from Republicans critical of the ACA, including Arizona Sen. John McCain. He introduced a bill meant to “protect AZ from Obamacare collapse,” according to a press release. Obama administration officials said they believed the situation would be resolved.

In September, Blue Cross Blue Shield of Arizona announced it would continue to sell exchange plans in Pinal next year after all. The decision came after state and federal regulators “expressed their concern for Pinal residents,” though the insurer made the call on its own, says Blue Cross’s Mr. Stelnik.

Neighboring Maricopa County, the state’s most populous, also ended up with just one insurer—Centene, Health Net’s new parent, which announced Sept. 14 it would sell exchange plans there next year. Centene CEO Michael F. Neidorff says his company has a very different approach from Health Net, which he says “thought they would get the revenue, the growth,” and relied on ACA risk programs for protection. Centene said it expects to be profitable in Arizona, as it has been in other exchanges.

That left only one county in Arizona, Pima, with more than one exchange insurer—it has two. There will be a few more options sold outside the exchange, to people who don’t get federal subsidies.

Premium increases are steep, though the effect will be blunted for those who get subsidies. Blue Cross’s rates are up by an average of 51% from this year, Centene’s Health Net unit’s, by nearly 75%.

Mr. Walton, the consumer who benefited from lower premiums at the start of the exchange, worries he won’t be able to find a plan that includes his primary-care physician and his cardiologist. “I don’t know what’s going to happen come November,” he says.

Write to Anna Wilde Mathews at anna.mathews@wsj.com