If the tires are truly going flat while riding it might be the inner tubes or the valves have gone bad. I had this problem with my mountain bike after I had left it sitting for months. Rubber can break down a bit over time, and bad valves won't hold the air in the tires.
As for bikes in general, I'm 265 and just test rode a Trek Lime on Sunday no problems except my legs muscles certainly weren't used to it.

I had to special order to get the color I want, and it should be in tomorrow. I'm so excited! I'm planning on biking to work a few days every week.