multiple requests to sign in to iCloud

One month ago I bought a MacBook Air and after setting it up with my iCloud ID and password I am asked by Apple to provide the password to iCloud multiple times each day by my MacBook and iMac, especially after a restart. I can be asked more than 10 times before I can get access to iTunes for example, after restarting the MacBook or iMac. My iPad, iPhone and iPod Touch do not make the same requests.

Has anyone else encountered this problem and how did you overcome this?