There is a problem with CRM if a policy forces a user to change passwords every XX days or when you change your Universal Hosted Cloud Services password. When this happens, the authenticated password for connecting to CRM 2013 via the Outlook plugin fails. You just get a screen that says CRM disconnected, but no prompt for a new password.
When you select “remember password” a new entry in the Windows Password Vault is created for you, which is why you don’t get a new prompt – the Windows password vault is still passing the “old” password for you. If you selected “remember password” when setting up your client settings, then whenever you change your password, you will need to open the windows password vault and update (or delete) the entry for “Microsoft_CRM_https://%your_URL_%
In windows 7/8, click Start, search for “Manage Windows Credentials”, or just enter “Vault”, or “Credentials”, click on the search result for Manage Windows Credentials and looks for the mentioned entry under “Generic Credentials” and you can delete the entry, which will cause Outlook 2013 to prompt for the password the next time you open and close it.