My IMAP mail now seems to be back in order, and I'll explain what I did in case it'll help others:
I tried to follow the instructions in the link you provided ("Alert Msg: 45 (1032) That Mail is not currently available."
However, when I tried to move messages to a new folder, it would move a few, then hang, so I gave that up.
Next: I tried a POP account that I'd created some time ago for AOL Mail, and started downloading messages. It would download a lot of messages, then hang with this error:
"The RETR command did not succeed. Error retrieving a message. Mail server
pop.aim.com
responded: system failure: IOException while retrieving content for item [27817533]"
I went back to AOL webmail. I found the date area of the last successfully downloaded POP message, and tried to open the message above (newer than) the last message retrieved in POP. It wouldn't open, however, I was able to delete it in Webmail. I returned to the POP account and started downloading messages again until they stopped with the same error as above, and repeated by deleting in Webmail a few messages around the last good one. I had to do that a total of 3 times, I think. I also found some messages that had invalid dates: they showed up with today's time, even though they are months old, and I could find the actual dates only in full headers.
When the count of POP mail was similar to the IMAP count, I went back to IMAP. It started downloading messages, or at least giving download counts in the "Inbox - Downloading" line at the lower left of the window. When it completed, I was able to go into the IMAP Inbox without an error. When I went to the Trash folder, I got the error, no doubt from some of the "bad" messages deleted. I went back to Webmail, and went through the Trash, since there weren't a lot of messages left. I found 3 or 4 that I couldn't view or open, and deleted those. (Emptying the Trash probably would have done as well.) After that, the IMAP Trash refreshed, and I no longer got the error.
It seems to have come down to identifying and removing messages that somehow became corrupt. I'm not sure how I'd have gone about this without the POP account when dealing with thousands of messages.
At this point, I'm not getting errors in any of the IMAP folders. I'll watch it over the next few days, and hope it's fixed.
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David