Went back and found what looks like a clue in an old
private email thread. Here is the salient excerpt:
"The app asks for the list of UIDs (identifiers, they're fairly short,
numeric) of ALL unread messages -- so it can count how many there are
and show a *server side* unread count, per folder."
So "mikeone", in future, please keep your ignorant assumptions private; they just confuse the issue for everybody else. And Kostya, you must have forgotten our email discussion entirely.
Anyway, thanks Kostya, as you seem to have hit it on the head with that. I must have lost interest in our discussion last spring and never read the last message. My advice is to make this behavior optional as it is clearly the cause of my issues. Will post back after going through the drudgery of telling GMail to mark them all as read. It will do maybe 10-20K at a time and then throw an error like clockwork. Tried repeatedly to do this operation in Aqua Mail and it never took. I figure that will do it. Thanks again!
One other note for those interested in the behavior when you have an extraordinarily large number of unread messages. It appears, as Kostya alluded to in the same email, that most email clients do NOT ask for the entire list of IDs. I went around to every email client in the house and did find one other (a dusty old MacBook Pro that I rarely use) that seemed to be timing out in similar fashion. Again, this should probably be an optional feature; I, for one, don't care about the unread message counts. Another suggestion is to use more descriptive error messages (preferably in the client, but certainly in the log). "Network Error" doesn't help diagnose the issue. Something like "Timed out retrieving unread IDs" would have solved this last spring. Granted, it's better than what the Mac does in this case; just leaves a little clock icon by the folder forever. Another suggestion: get the messages
first, then get the unread counts (when possible). A timeout getting the unread counts should not prevent the client from getting new mail.
I admit I have been hard on you here, but I use this app for automation with Tasker and hate it when apps work for a while then inexplicably fail with vague error messages. When it works it is almost perfect; apologize for calling it a PoS in an earlier post. The one thing I still don't get is why the push isn't working for me. Surely it doesn't try to get this unread ID list during a push operation. (?)
Also, this forum lost one of my replies on a session timeout. Had to type it all over again.