I'm having the same issue as the others here. About a month ago I bought the iPhone 12 to replace my aging iPhone 6sPlus. On the 6s I was up to iOS 14.2 and never had the constant "please sign in" problem.
When I changed over to the iPhone 12, I restored the phone from my iTunes backup, and then updated it to the latest (as of this writing) version, iOS 14.3. From this point on I am repeatedly asked to sign in (sometimes twice a day) even though I never signed out. Two or three times a week, after the sign-in attempt, the phone tells me my account is locked and then I have to go through my security questions to get the phone unlocked and useable again. After this, a few days will pass before I'm asked to sign-in again, and then another day or two will pass before I am locked out again and have to go through the security question BS all over again. This is freakin MADDENING!
IMHO this is clearly a bug in iOS. Here's what I have tried to remedy this:
- Sign out then sign back in to my Apple account via my phone
- Sign out via my Apple account online (via my computer), and then sign back in on my phone
- Sign out of my account, change my Apple ID password, and then sign back in again
- Went into Settings > General > Reset and used the "Reset All Settings" option
None of these things have solved the problem. Come on Apple, PLEASE fix whatever bug is hiding in iOS 14.x and help us out here.