iCloud rejects CORRECT password when logging in

Every time I log in to my computer (or restart), I get a window that asks me for my iCloud password. Even though I enter it correctly, the window “wiggles” and clears out the password. Multiple attempts to re-enter the password results in the same symptoms. I’ve even reset the password and tried with this new password and the same thing happens. The only way to make the window go away is to click on Cancel, not once, but twice. I know the password is correct, because I can go to iCloud.com and log in successfully. That same password also works with my Apple ID any time a password is requested, further reassuring me that I’m using the correct password. Why is it continually being rejected at login?