+ AA6YQ comments below
Thank you, Dave. I just did this again so that I could explain it carefully. Hopefully, this is useful at some point. I'm delighted to be discussing this, thank you.
I selected "Sync LOTW QSLs." The progress dialogue pops up and halts at 59 seconds. The title bar displays 'not responding,' and shortly thereafter, the windows dialogue comes up, saying the same thing and offering a choice of stopping the program or waiting. I select to wait. The DXKeeper windows (main, capture, and the QSL sync progress) are shaded. I have been waiting 35 minutes with no change.
Memory is 41% utilized, CPU is 40%, Disk and Network are 0%, and GPU is 8%. I don't have the skills to look into the number of open file handles, etc. But there are no other evident issues with closing, opening, and using numerous applications that would consume additional resources, open file handles and network connections, allocating memory, etc.
I'll keep at it. It feels like a blocking issue. One day I'll find my gremlin. :) Thanks again, sir!
+ The fact that Windows displays a separate window offering to stop DXKeeper or continue waiting is also unique to your situation..
+ You have reported that the LoTW Sync functions work if you start DXKeeper immediately after rebooting Windows; that likely rules out interference from anti-malware or firewall applications automatically started by Windows, since they were running when you reported success.
+ If you (understandably) cannot diagnose Windows yourself, then I suggest engaging with Microsoft Support to obtain their assistance in tracking down the root cause of this behavior.