Macbook Air AppleID problems

Everytime I turn on my Macbook Air (or wake it from sleep mode) it is telling me I need to re-enter my AppleID password, and then constantly asks for verification codes supplied to my iPhone. I have changed my AppleID password across all my devices in an attempt to resolve the issue (I have an iPhone4s and iPad mini - these seem fine), but I still keep getting the notifications which is really annoying and a waste of time.