Dealer said he couldn't see a problem. (I have no actual proof that he actually looked.) I have a nice plug-in tire pump (the $35 one from Harbor Freight; the cheaper one burned up rather quickly when I tried to pump all four tires) so there's no real problem, and I'm unwilling to load the tire up with slime, but I'd really like to know WTF is happening. Sooner or later I'm going to need new tires and it would be nice to know if I need a new pressure sensor too.
BTW, I really like the tires (Goodyear Eagle RS-A) -- excellent cornering on the road I take to go skiing. People really need to be ashamed when they get passed by a granny in a 9-YO Corolla!