Are your multiple addresses with the same email provider? A while back there were many customers of GoDaddy posting on this forum and reporting this behaviour, and a couple of weeks ago there were at least two customers of Virgin Media reporting it too. The problem may have started after your recent Thunderbird upgrade but don't assume that's the reason.

Thanks amanchesterman. If you are indeed a Mancunian I'll forgive you for being the wrong side of the Pennines. I have multiple addresses through three different domains. Two are housed by one hosting service. The third, through my ISP, appears to be working OK. When I start Thunderbird, and I've gone back to 31.8 to see if its the latest release that's causing the problem, all email addresses are checked OK and all mail that's available is collected, but when I force a mail check, because I suspect something should have come through but hasn't, I get "connecting to ..." then nothing. There have been times when I have checked using webmail and seen messages which should have been collected. When that happens I shut down Thunderbird and restart it - and get those messages. I also, occasionally, get a request for a password for one or more of the addresses, but if I just cancel on that attempt I don't get the same message on a repeat attempt.

The fact that I can get all emails without problems when I start Thunderbird is a clear indication that the problem isn't with the hosting service, especially as I can see emails by using webmail after they should have been picked up by Thunderbird.

I have virus scanning active, regularly check for malware and spyware, and have checked the registry in case there are errors there. Because I am using Windows 10 personal version I haven't a clue what impact any upgrades to Windows might be having - which is one reason why I object to Microsoft determining what updates I'll get and when.

I will persist with restarting Thunderbird every time I suspect mail should be showing but isn't - and that can be several times a day.

The fact that I can get all emails without problems when I start Thunderbird is a clear indication that the problem isn't with the hosting service, especially as I can see emails by using webmail after they should have been picked up by Thunderbird.

You're drawing the wrong conclusion. If the server tells Thunderbird there are no new messages, then Thunderbird cannot retrieve any new messages, even if there are new ones on the server. That was the problem with the GoDaddy server which did affect so many people, and GoDaddy were simply denying there was a problem. In the end they silently fixed it though, whatever the problem was. So you should talk to your email provider.

GoDaddy reference fyi: https://bugzilla.mozilla.org/show_bug.cgi?id=1260724#c10