When the system clock loses time, it could be due to HW, SW, or Windows itself.
The fact that you just replaced the battery and the clock kept time for about a week would eliminate Windows unless you use your computer once a week.
It must be either HW or SW that are not used everyday. You need to think or remember what HW or SW may be used maybe once a week or so.
This could be, for example, an antivirus program that may be updated the virus definition once a week.
Or it could be a sound card or CD-ROM / CD-RW / DVD-ROM that you use to listen to your favorite audio CD (or Movie) maybe once a week.
You have to come up with potential culprits and test one at a time to resolve your problem.
To test if it is the antivirus program (if you have one), go to the manufacturer?s website and search if there?s any patch.
To test if it is the CD-ROM (assuming it is not used everyday), disconnect it and see if time keeps up beyond a week.
Now you get the idea. Hope this helps.