On our SharePoint servers, we were seeing the following errors:

Event ID: 7888
Source: Office SharePoint Server
A runtime exception was detected. Details follow.
Message: Cannot open database "SharedServices_db" requested by the login. The login failed.
Login failed for user 'DOMAIN\ACCOUNT'.

Event ID: 7888
Source: Office SharePoint Server
A runtime exception was detected. Details follow.
Message: Access Denied! Only site admin can access Data Source object from user profile DB.

Event ID: 5555
Source: Office SharePoint Server
Failure trying to synch web application 10971c0f-3cf0-4be7-8a13-04222d05cf14, ContentDB 74c4483f-53d8-4f2d-9bed-98e6cbca387f  Exception message was Cannot open database "SharedServices_db" requested by the login. The login failed.
Login failed for user 'DOMAIN\ACCOUNT'.

This was probably two reasons for this, and the two actions that can be carried out:

# Ensure that within the SSP you have granted your default access account and the SSP application pool account manage profile permissions. To do this, go to Central Administration > SSP > User Profiles and Properties > Personalization services permissions and add the default content access account and provide the "Manage user profiles" permission.

# Run "stsadm -o sync -deleteolddatabases 0" (in our case we had been deleting and restoring SharePoint databases and it was most likely still trying to sync with a database GUID that was no longer valid.