Or maybe I should get some new tires?
The tires are OEM. The bike is an '06, bought new in '08, but largely ignored until last year. They look like to be in decent shape still, but I've been averaging like 1 flat a week for the last 2 months.
The latest flat revealed nothing- nothing in the tire, the wet test on the tube showed no escaping air. I put a new tube on the bike and let the old one hang in the garage to dry overnight. It's now flat again ( or has less air in it now than it did 24 hours ago).