Are you using Active Directory or LDAP for your user authentication for ArcGIS Server? And, are you using a network user to authenticate that has to change the password every XX number of days?
If so, then you will need to reapply the authorization (in the security tab) every time the password of this network user account changes. They recommend a "service account" were they password never expires (but getting an account like this from IT can sometimes be a challenge).
If this is not the case, can you give more detail on whether it is your account password that you are thinking is change or the Primary admin account?
