When you've recently changed your password, you will continuously be prompted to type in your password everytime you want to sync, and you don't see an option to always be signed in.
To resolve, you have to select to sign in as a different user, then re-enter your credentials. Signing in as a different user will show the checkbox to enable always be signed in. This method won't affect your synced data.
You can disable the password expiration for one or more users through Powershell.
$cred = Get-Credential Connect-MSOLService -credential $cred Get-MSOLUser | Set-MsolUser -PasswordNeverExpires $true
Note that you need to have the Microsoft Online cmdlets: http://technet.microsoft.com/en-us/library/jj151805.aspx