I was having problems with a tire on my Civic awhile back, it seemed fine one minute, then coming back out after eating it was completely flat. Sears tried 3 different times to find the leak(they were the only place open on a Sunday morning and I returned there the other times since they’d done it before), on the 3rd time, they said that I should take the tire back where I got it and get a refund or replacement. They dunked it in water and resealed the bead each time to no avail. A relative suggests taking it to his mechanic and having him look at it, after I had already ordered my new rims and tires. We get there, the guy pumps the tire up almost to the max on the sidewall, and he finds there’s a small hole on the rim as well as the tire that was leaking. He patched the tire up for me and sent me about my way.
If your car is old enough, you may have a rusted hole in the rim itself, or a VERY tiny hole somewhere. If they are old aluminum rims, then they’ve probably become too porous and are leaking