Here's what the two incidents have in common: 1) It was my heaviest-flow day. 2) The cup was nowhere near full, so it wasn't a capacity issue. 3) The problem didn't start until I'd done some walking (to the post office and back, both times). I'm thinking it might be a distance thing, because when I've walked to the bus stop (significantly closer) on my heaviest day I had no problem. 4) I'm not sure how important this is, but both times my period was also weird in another way: it started the night before what I would have called the first day, and was lighter than normal throughout.
This time I really looked at the cup before dumping and rinsing, and it looked like there was actually blood trickling through at least one of the holes! Even though it was only about half full. I'm sure it wasn't residual slobber because I wipe so thoroughly before reinsertion that I don't really have any. I also always make sure the cup is fully opened before I leave the bathroom (I've found the easiest method of insertion to be sitting on the toilet and using the punchdown fold).
I've walked that distance while using a cup before without problems, so I don't understand what's happening now. Any thoughts?