Try to start Windows in safe mode with networking enabled. - Win10 https://support.microsoft.com/en-us/help/12376/windows-10-start-your-pc-in-safe-mode

Still in Windows safe mode, start Thunderbird in safe mode. - https://support.mozilla.org/kb/safe-mode

Does the problem go away?

I'm not sure what has happened (I didn't do anything - honest guv!) but this morning previously blocked e-mails were downloaded without problem! I had not gone through the safe mode routine, no point if the problem has self corrected?.

If the problem recurs I will try the safe mode routine and report back if that's OK? Incidentally one of the previously blocked messages was the Mozilla registration verification e-mail!

If the problem recurs I will try the safe mode routine and report back if that's OK?

Certainly, yes.

I have found that rebooting apparently "clears" the problem, whether in safe mode or normal mode (I've tried many times using both reboot methods) So rebooting in safe mode doesn't seem to make any difference? The problem recurrs, almost daily. It does not seem to be related to the size or source of the e-mail (very PC!) Also it appears that if I go to the server site, move the "offending e-mail" to a holding folder & then move it back to the inbox it will sometimes then download without problem?

I have found that rebooting apparently "clears" the problem

It apparently doesn't fix the problem.

So rebooting in safe mode doesn't seem to make any difference?

The most likely cause for your problem is anti-virus software. Windows safe mode disables anti-virus software. So booting into safe mode is not the solution, it is just a temporary step to diagnose the problem.

Some general recommendations wrt anti-virus software: Create an exception in your anti-virus software for the Thunderbird profile folder, so that the anti-virus real-time scanner will not scan it. http://kb.mozillazine.org/Profile_folder_-_Thunderbird

Don't let your anti-virus software scan incoming and outgoing messages.

Don't let your anti-virus software scan attachments.

Don't let your anti-virus software intercept your secure connection to the server.

Remove any add-ons your anti-virus software may have installed in Thunderbird.

Keep it working. http://kb.mozillazine.org/Keep_it_working_-_Thunderbird

I have tried all your suggestions and nothing seems to resolve the problem. I am now upgraded to Thunderbird v56.0b2 (32 bit), which for a day or so I thought had fixed the problem - it didn't! I am using W10 Home v1607 64 bit with Norton Security 2017 which is up to date. The problem usually occurs at least once per day. I go to my ISP server to check important e-mails & then reboot, which clears the problem every time, until the next time. There doesn't appear to be any consistency to the number of e-mails received or the amount of time Tbird has been running before the problem occurs.

I have tried all your suggestions

Please explain in detail all the steps you did.

I excluded the Tbird profile folder from AV scans. I barred Norton Security from scanning inbound/outbound messages. I barred Norton Security from scanning attachments. I disabled Noton Security to prevent interception of the secure connection to the server. I disabled ALL addons to Tbird. I virtually emptied the Inbox - filing messages in other folders. I empty the Trash folder regularly. The Junk folders are empty. All folders are regularly compacted. The profiles folder is regularly backed up to a cloud site. I have 50% space on my C: drive, 75% space on my storage drive. I have Adminstrator privileges as the only user.

Well, there isn't much more to suggest then. May be you should ask in a Norton support forum. Also see https://wiki.mozilla.org/Thunderbird:Testing:Antivirus_Related_Performance_Issues#Norton_Security