Solution 3 if you are using POP, and I think you might well be as you are talking of a popstate.dat file, is disable your email scanning component in your antivirus (Norton in particular has troubles with pop mail). The antivirus encounters a malformed email, which is usually spam, and instead of moving on it crashes. Than a little later (15 minutes by default) the same email download again and when it gets to the problem one it crashes again. Each crash results in a timeout, not a got mail event, so Thunderbird never gets to update its popstate.dat file that it got any email.

BTW, I have no idea how to implement your solution 2. There is no function to do that as far as I am aware.

I do have to wonder if you moved your old mail data to your new device https://support.mozilla.org/en-US/kb/moving-thunderbird-data-to-a-new-computer or if you set everything up afresh and now the new Thunderbird is now downloading your archived mail from the last however long because you never deleted any of it from the server. That would be entirely normal, but there are folk who think that because they know they have seen it they can tell the server to just get mail after a certain date. POP does not work that way it just gets everything that is waiting on the server that that installation has not already retrieved.

Thanks Matt From your email, I have learnt that popstate.dat is associated with the POP protocol. In fact I used IMAP not POP; so I now know that popstate.dat is irrelevant to me.

But I wonder if there is an equivalent file under IMAP, ie with the same function: to record which emails have already been sent from the server. This function must exist but it's going wrong on my machine!

(IMAP automatically leave all my emails on the server. I like this as I access them from different machines, different software. with my actions synchronised across the machines. )