Like many of you, I've come across many of those little gotcha's in security and setup of SharePoint 2010 - one of which has been issues with teh FIM services and the User Profile Synchronization (including sometimes when the connection seemingly disappears). I did find an excellent post so reposting the answer (with due credit) here:
1. For the Event ID 1004:
The reason that we are seeing this message is that the WMI calls are made under the credentials of Network Service account and it doesnâ€™t have permissions to the folder in which Microsoft.ResourceManagement.Service.exe is located and thus the resource not found error is logged.
The error should go away if the Network Service account is given permissions to the folder (as indicated in the error)where the resource is located. (C:\Program Files\Microsoft Office Servers\14.0\Service)
2. For the Event ID 5555:
a. Go to the user profile service app, click on the Administrators button in the ribbon and give Profile sync account Full Control rights
b. Then click on the permissions Tab and click and give that account full control there as well.
c. Do an IISReset and monitor to see if the errors go away.
Fred Ellis - MSFT