iMac mail only receives iCloud mail when starting

I have several strange point which has recently turned up on my iMac mail.

I have a number of accounts, which all work perfectly - except the main icloud account! Here are my findings:

• All mails are send correctly.
• The mail program will only retrieve new mail from my iCloud account when the mail app is started, and no new mail is read after that. (I have have upgraded my iCloud space with lots of free space)
• When mail is started, a massage "Moving messages, 1 out of xx" (in Danish) appears and the message is shown permanently whenever the mail app is open. I have not defines any rules for moving mail.
• If I activate the the account menu item in the mail menu, the mail program will suddenly read new messages. It is enough to show the menu, no action is required!
• My iMac is an older model running macOSCatalina, but this has not created any problem until the problem described above started.

Any help will be appreciated