Technically, you can't set up out-of-office for shared mailboxes through a normal way, because you can't log in with Outlook on those accounts. A workaround would be to temporarily convert it to a regular mailbox, grant a license to it, and then log in with Outlook, but this is not always possible or desired.
Fortunately, you can also enable out-of-office through Powershell on any mailbox, including shared and resource mailboxes.
UPDATE: this article has been merged into Configure DNS for Office 365 using DirectAdmin → Configure Lync Online.
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