You may have exceeded the maximum number of connections to this server. ..." Apparently this is due to the fact that I have too many folders/messages saved.

I doubt it.
Make sure there are no other devices accessing the IMAP server simultaneously, e.g. another instance of Thunderbird, or a mobile phone.
For Thunderbird you can limit the no. of server connections in your Account Settings.
At the top right of the Thunderbird window, click the menu button > Options > Account Settings - Server Settings - Advanced - Maximum number of server connections to cache

Is the phenomenon of there being no mbox file, when the associated folder has subfolders, a "known issue" or are the Computer Gods singling *me* out for persecution?

Neither nor.
Is there any message in the "Misc_Lists" parent folder? If not, try to copy a message there, and see whether a mbox file Misc_Lists is created.

Note, you'll have to turn on synchronization for all the folders you want to import into Local Folders. Otherwise you may just import message headers, but not the bodies.
https://support.mozilla.org/kb/imap-synchronization

Thanks very much christ1. But I'm still stuck.

(1) The bit about "Apparently this is due to the fact that I have too many folders/messages saved" is what the IT people at my university told me. I have no real idea.

(2) I have previously fiddled with the "Maximum number of server connections to cache" adjustment. I have increased and decreased it, with no effect. Currently it is set at 2. What is a "reasonable" number?

(3) I am *certain* that "there are no other devices accessing the IMAP server simultaneously". There is no other instance of Thunderbird possible (I am the only user; "ps aux | grep thunder" reveals only one instance of thunderbird running on my laptop). I do not use, or even own, a mobile phone.

(4) There are *loads* (!!!) of messages in "Misc_Lists".

(5) I don't think that synchonization is involved. When I import a single mbox file/folder, with no subfolders, I get all the messages copied over, no problema. However I will look at the synchronization link that you provided and see if I can make any progress.

(6) I'm pretty sure from what you have said that the Computer Gods *are* singling me out for persecution. :-) The absence of mbox files (such as Misc_Lists) and the presence only of the directory Misc_Lists.sbd and the index file Misc_Lists.msf, is a pretty clear indication of this. It doesn't happen to anyone else, does it?

Thanks again for your efforts. If you have any further ideas I'd love to see them.

The problem seems to have resolved itself (spontaneously ???) overenight. I am no longer getting those "Unable to connect to your IMAP server ...." messages, and email is showing up in my inbox.

However a possibly coincidental problem arose. Whenever I deleted a message, the delete would hang for an indefinite amount of time. Although it's not clear what relation if any there is between this problem and the suggestion made by christ1 that I investigate "synchronization", I decided that I give this suggestion a go. So I went to the appropriate spot in the menus and changed "Synchronize all messages locally regardless of age" to "Synchronize the most recent [12] [months]". This seems to have had the desired effect in that deletes are now instantaneous.

Note that the phenomenon of there being no mbox files present, when the folder in question has subfolders, persists. Since I am no longer pursuing the strategy, of copying folders to my "Local Folders" and deleting them from their original locations, this doesn't really matter any more. It still makes me nervous, but.

Since christ1 said that he had never observed this phenomenon, it does indeed seem that the Computer Gods are singling me out for persecution. :-)

Be that as it may, the problem(s) seem to have been rectified, and I guess this enquiry should be considered "solved".