An activation prompt means the product genuinely is not activated. There is no half licensed state where some features quietly lapse, so what you are seeing is the activation state being wiped rather than anything wrong with your key or your account.
Fences and Start11 both doing it is the useful clue. They share the same activation mechanism, and each product keeps its licence files in its own folder under %ProgramData%\Stardock. Something on the machine is removing them, which is why re-entering the key works and then stops working.
The usual cause is a cleanup or optimiser tool. Some of them have bugs that clear the activation state as unneeded files, and IObit Advanced SystemCare has turned up in a thread with exactly this shape, though any of that family can do it. Do you have one of those installed, particularly on a schedule?
If you do, deleting the folder again will not hold. Add %ProgramData%\Stardock to that tool's exclusion list first, then activate once more so the files it writes are the ones that survive.
The other thing worth ruling out is Controlled Folder Access, under ransomware protection in Windows Security. It stops our apps writing files where they need to, and that produces the same never sticks behaviour.