The password is stored locally on the ePo server - so changing it will cause authentication between it and SQL to fail.
Try to navigate to https://servername:8080/core/config. Does this work? If so, change the password that it authenticates with to the new password. If it doesn't work, and the Administrator password is something you change often, I'd consider using a service account to keep the connection live at all times - and assign the account permissions based on what it needs to access within SQL.
There is a file on the ePo server that contains the encrypted password, the name and location of it escapes me at the moment. You could also replace that value with the encrypted password from within the database and it should start working.
I'm still learning about ePo myself, so someone else may have a better / more complete answer, but this should get you working. I'm not sure what 100% sure best practices are in this situation.