Problem with iCloud account on MacBook Pro

Every morning for the past month, I have gotten a notification on my MacBookPro that iCloud Drive cannot be used because there is a problem with <my appleID>. Until this morning, when I tried to sign in to my iCloud account to fix the problem, I was told that my password was incorrect, even though it was correct. I ignored the problem until this morning, when I decided to click "Forgot password" and tried to reset my password. After resetting, when I tried to continue, I was told "An unknown error has occurred". I guess that's better than being told that my password was incorrect when it wasn't! But it is still no closer to a solution.

And when I later tried to sign directly into my iCloud account from System Preferences, I was still told that my password was incorrect, even though I was using my updated password. So I changed it again, and then signed out of iCloud and tried to sign in again. Now, trying to login fails silently after I enter my password: in other words, it takes me back to the step where it displays my appleID, prompting me to click Next, and clicking Next then brings up the prompt for my password once again.

What could possibly be going on here?