Thanks again for all the comments. The rim is single wall, and because of the work I had done, I was sure that the spokes or foreign objects weren't causing the flats. At one time or another both the front and rear tires had gone flat -- a couple of times both at once. I tried the talc powder and slowly inflating (actually I partially inflated the tires and bounced them a few times and then finished inflating them) --- that seems to have worked. Apparently the tube, when fully inflated, was stretching irregularly and that led to the flats. The talc lets the tube slide inside the tire and rim and that fixes the problem. Hurray! I can once again use the beater for short local errands.