Rents skyrocketed in 2014 and many analysts did not think those escalating costs would be sustainable. But they have yet to slow in 2015 – and in fact, rents have gotten higher -- and the increases likely will continue into next year.

Annual rent growth in September was 5.2 percent – the highest since 2011, according to Axiometrics, an apartment research firm. That also marks the eighth consecutive month the rate has been 5 percent or higher. A year ago, annual rent growth was 4.1 percent.

Read more: Why the Rental Picture Looks Grim

"The eight months the rate has been above 5 percent is the longest sustained period of strength we have seen,” says Stephanie McCleskey, vice president of research at Axiometrics. “The last growth cycle was only four years, and this cycle is already five years long — with no sign of stopping.”

Apartment construction has been increasing to meet rising demand, but some say it’s still falling far too short.

"New inventory coming to market is weighted to the high end; it's urban, Class A, with a rich set of amenities, targeting the coveted college-educated millennial," Sam Chandan, president of Chandan Economics, told CNBC. "Overall, we still have an affordability crisis in the United States with rents rising faster than incomes for the fourth-consecutive year."

In September, apartment vacancies were low – at 95.3 percent occupied nationally. Axiometrics considers anything above 95 percent as a “full” market.

But weak income growth may not support rent growths much longer in some markets.

"There is only so hard you can push on rents," Chandan says.

Some studies are showing that it is more affordable to buy a home than rent. But inventory constraints in the for-sale market – particularly on the lower end – can keep renters renting, as well as the inability to save for a down payment due to the high rental costs.

Lately, rent gains are highest in cities with boom tech sectors, such as in Seattle, Denver, and Portland, Ore. Rental prices are also above average in Nashville, Tenn., Charlotte. N.C., and several cities in Florida, Axiometrics reports.

"Younger, newly formed households continue to move out of their parents' or roommate living arrangements and rent an apartment, driving up the demand for more rental units," says David Crowe, chief economist for the National Association of Home Builders.

Meanwhile, homebuilders – such as Lennar and Toll Brothers – are adding more rental apartments to their mix.

“Thirty-five percent of new home starts in 2015 have been multi-unit,” CNBC reports. “That is higher than a year ago and the highest share since 1973. Developers are simply going to where demand is highest and most lucrative.”

Source: “Think Your Rent’s Too Darn High? Just Wait,” CNBC (Oct. 20, 2015)