The past two days of orders have come through ok. I am reluctant to proclaim that the problem is solved because this happened before, and then the problem kicked in again. The problem seems to hit glumps of transactions. But right now it seems to be ok.
No, I have never had to do anything to make the process happen. It just happens in its own good time. In every single message that I have written to PP, I have noted E-J -- yeesh, you'd think they would pick up on it eventually. (When I reported the issue to PP, they told me to contact the Developer Support division, which is probably what made the support person think I am a developer, even though I told him I am not.)
No, I've looked for consistencies -- credit card pay vs check, country vs country, product vs product, etc, and I can't find a common element.
I'm going to leave everything alone right now and see what happens. It may miraculously be fixed. If not, I'll be back. Thanks for your patience on it.