No voltage from breaker even though breaker is good
Sorry for the slow response, but when in the process of taking out the breakers to investigate the bus bar I figured out what was going on and it took me a few days to confirm it. The two bad breakers were in the same row of my sub panel, and it dawned on me that if one the lines from the main panel that feeds sub panel was bad, that could be causing my problem. So I tested the two breakers (tandem) in the main panel that were feeding my sub and sure enough one of them was putting out 25V. So I replaced the tandem breaker in the main panel and now everything is working agin. 

Thank for your suggestion about the breakers being in the same row, which got me thinking about the problem in a different way.