Why does iCloud constantly ask for my password?

iCloud had worked perfectly on all my devices and then a few days back it started asking for my Apple ID password at least once per day on all devices. Sometimes it asks more than once per day, which is extremely annoying. Two days ago it would not accept it and locked me out. Apple phone support said to wait 24 hours and try again, which worked. However, I get asked all the time yet to enter my Apple ID password. Is there a way to get it to remember this ongoing? Thanks.