I was having this issue as well on Windows 10 Enterprise ( my current version 10.0.19045 Build 19045 )
I use iCloud with Microsoft Outlook email program.
The fix for me was to sign-out of iCloud on my computer.
And I ensured that all iCloud, apple, & bonjour apps & services were stopped on my computer.
- Open Task Manager [ shortcut = ctrl + shift + esc ]
- In Task Manager;
- "iCloud xxxxx" and "Apple xxxxx" named items were in the "processes" tab and "details" tab.
- The "Bonjour Service" was in the "Services" tab.
- Find the named item in whichever tab, right click it and select: "End Task"
- Also, when you open "Task Manager" , you may need to select the "More Details" at the bottom of the window to see everything I am mentioning.
This stopped the login prompts completely.
But since I actually use this service, I was able to start the iCloud app and login successfully this time.
So far I have not had a popup for logging in again.
I am guessing that there is probably a time-out period for the login session and this issue will resurface again in a few weeks.
Here are a few other forum posts about this issue that may be helpful if my fix does not help.
https://discussions.apple.com/thread/8061821?sortBy=rank
https://discussions.apple.com/thread/8369914?sortBy=rank