Bay Area home sales drooped in July to their lowest level for that month in six years.

And guess what? As the housing supply continued to dry up, home prices kept climbing on a year-over-year basis – up 10.1 percent for the region, even in the supposed doldrums of summer. A typical Bay Area single-family house now costs $804,000.

“These prices have been going up at a good clip for years now,” said Andrew LePage, research analyst for the CoreLogic real estate information service, which released its July report Wednesday. “They’re rising at a faster pace this year than last, and that reflects the very low inventory that exists in most markets, along with steady buyer demand.”

With a single exception – in May 2016 when prices stayed flat – the region-wide median price for a single-family house now has climbed for 64 consecutive months. Many homeowners are holding tight, because the idea of moving to another house in the region seems like an impossibility – even 1,000-square-foot bungalows are selling for well over $1 million in parts of Silicon Valley.

Yet the run-up is enough to prompt a few sellers to cash out: “I just figured this market couldn’t go much further,” said Michael Lecy, a firefighter in Sunnyvale who just sold his home — purchased for $700,000 in 2004 — for $2 million, all cash. “I just didn’t want to get short-changed. It seemed like the right time.”

Reflecting the low housing supply, July home sales dipped 1.9 percent year-over-year across the region – and more steeply in some counties, including San Mateo (down 9.9 percent), Contra Costa (6.7 percent) and Alameda (6.1 percent). Sales even fell 3.9 percent in Solano County, where the median price was $410,000, the lowest in the region – yet up 13.9 percent from the year before.

Santa Clara County was the puzzler: Even with about 30 percent fewer homes available than one year earlier, sales were up 13.0 percent. LePage offered a hunch as to why: “Buyers are burning through whatever inventory there is, really fast.”

Still, the affordability crunch is pushing many potential buyers out of the competition. Not only have prices climbed 10.1 percent year-over-year across the region, he said, but rising mortgage rates – up about half a point since last year – have boosted the typical monthly mortgage payment on a median-priced Bay Area home by more than 17 percent.

In July, the median price of a single-family house in Santa Clara County was $1,097,000, up 11.0 percent year-over-year. San Mateo County’s median sale price was $1,310,000, up 4.8 percent from July 2016, while Alameda County’s median was $825,000, up 11.2 percent, and Contra Costa County’s median was $585,000, up 8.3 percent.

Kevin Kieffer, a Keller Williams agent in Walnut Creek, said, “Anything under a million that’s single-family is going to move within two weeks” in that city.

He noted that the scant inventory “has amplified” the usual seasonal slowdown: “You’re going to see the headlines soon,” he predicted. “`Sales plunge in the Bay Area,’ and it’s not because there aren’t any buyers. It’s because there’s nothing to buy.”

Not everyone is complaining. Agent Alex Seroff, of DeLeon Realty in Palo Alto, said the market “keeps supporting or even exceeding expectations.”

As an example, he cited his client Lecy, the firefighter whose house in Sunnyvale listed for $1.5 million, drew 20 offers and sold for $500,000 over asking.

More broadly, Seroff pointed to month-over-month, August median price increases for homes around the Peninsula: up 3.2 percent to $2.69 million in Palo Alto; up 4.4 percent to just over $4 million in Los Altos Hills; up 3.5 percent to $1.37 million in Sunnyvale.

Alain Pinel agent Mark Wong did a quick search of the Multiple Listing Service and found 37 properties that sold for at least $200,000 over the asking price during the past month in Sunnyvale. Prices keep going up in that once modest city, which is close to major tech centers, including the new Apple spaceship campus.

“Do you know who I feel very sorry for?” Wong asked. “It’s really hard for millennials to buy right now, even though they have very decent incomes. And that’s because of the down payment: 20 percent down on a $1 million house is $200,000, and who has that?

He added, “I have clients right now — both doctors — and they can only qualify to buy a townhouse. Doctors!”

Yet from time to time, the stars align.

Wong recently was contacted by different clients, Bee-Chung Chen, an engineer in tech, and his wife Shiao-Ching Chen, a homemaker. Their house in San Jose’s Cambrian neighborhood was feeling too small for them and their four children, ages 10, eight, six and 11 months.

They decided to look for a five-bedroom house and to set their budget at $1.5 million.

Off they went on their search.

The couple looked at a house in San Jose’s Eden neighborhood. It had five bedrooms, a swimming pool and a walled courtyard where the kids could safely play. It was “a little bit old and the sellers did not stage it,” Shiao-Ching said. “But for me, it suited our needs and I knew that through our efforts at remodeling, it could look pretty.”

The house listed for $1,475,000.

The couple bid $1,450,000. Theirs was one of just three offers.

And the sellers accepted their bid – an under-asking bid on the only property they had seen.

“It’s unbelievable in this market, right?” Shiao-Ching said, laughing. “I don’t know how to explain this. Probably not many people search for a five-bedroom home. Or else it’s God’s grace, I don’t know.”