The problem has mysteriously not occurred since I started this conversation. If it starts again I will definitely tyr your suggestion.

I am using Win 10 1909.18383.720.

Pegasus has begun freezing regularly. I have to use the Task Manager to delete it.

Your definition of "freezing" is important. 

If you see "Not responding" and consider that a "freeze" then you are probably killing the task for no reason.  "Not responding" normally equates to "I'm busy" and usually clears on its own.  The duration depends on the task Pegasus Mail is performing at the time.

Pegasus Mail files should be excluded from active anti-malware scanning to eliminate that potential interference. 

There's no message, rather the activity circle on the tip of the cursor keeps spinning and the app will not respond to any attempt to click any control. I've allowed this to continue for as long asn an hour and the issue doesn't get resolved. I use Windows Defender.

Did Pegasus ever run before with W10 installed, or did you install W10 the first time and since then Pmail is not running?

In case Pmail was working, also under W10, what were your last steps before the freeze occured? Did you composing an email, tried to send an email, tried to read a new mail, choosing attachments, give us some more feed

I also experienced "freezing" reproducibly on all computers which were upgraded to "Windows 10 Enterprise LTSC". I found by coincidence that the "freezing" does not occur, when I close Pegasus with "Folders" open in "Preview Mode". It amazingly occurs with "Folders" open in "List Mode". I can live with this glitch, but it is indeed annoying.

Yes, I've been runing Pegasus the whole time I've used Windows 10, which is from about 1 year after Win 10 was introduced (2015?). Freezing has never been a problem until the past month or so. That's why I included the precies version & build #s hoping someone might recognize the issue and connect to recent patches.

Interestingly, I experience the freezing when I close Pegasus withn all folders open in preview mode.

I'm not a Windows 10 user so I may not be the best "helper" here. Anyway, do you see any changes if you switch to the Classic mode? I also couldn't figure what is "all folders open in the Preview mode." Would it be the expanded Folders' treeview?

Yes. "all folders open in the Preview mode."

A hang on close sounds like it is waiting for a response, perhaps to one of those popup notices like is generated when there is a problem with a folder index.  Unfortunately I don't have a clue how to confirm this or make it visible. 

I would try a shut down of Pegasus Mail while in List mode with all folder windows closed except the folder list window.

While closing, Pegasus Mail writes settings to its config files like HIERARCH.PM and STATE.PMJ, among others. So it is most important that no other application (antivirus?) has access to Pegasus Mail files. Just to exemplify, my Kaspersky antivirus is forbidden to actively scan C:\PMAIL and its sub-directories. All malware control action on these directories is done through Virscan, a highly recommend Pmail add-on available here in the Community.

You most likely are using Windows Defender that can also be configured to avoid C:\PMAIL. And of course, Virscan is prepared to work with Windows Defender as well.

It hangs at unexpected times, not just at close.

Just guessing.  I have about 1400 emails in the deleted folder & a wondering whether that is causal. So I moved them into another folder. We'll see what effect that has.

The deleted messages folder is not the cause. It is something else. Try activating System Messages (under Window menu) and leave it open. It may indicate the action prior to the hang. As Brian mentioned behind may be the application waiting for something that never comes.