Media Center will UAC prompt to elevate privileges on first run if:
* It is the first run ever of that particular "major version" (19 vs 20 vs 21) or if it was the first-run since some other major version was run, AND...
* The application wasn't launched from the installer itself (via the Run installed program now checkbox), since the installer already has elevated privileges and can launch MC itself with them.
This is so that MC can register itself with COM, and correct the HKLM registry entries if required (perhaps among other things).
So, the most common reason you'd see recurring UAC prompts to launch MC is if you switch back and forth between an older version of MC and a newer one. You'll see it every time if you're still running the old version in Media Server mode.
If you see it outside of these types of situations, this is an indicator that something is going wrong with your installation. Perhaps a registry "cleaner" is messing up your registry entries, or some overactive security application is blocking (or making temporary) MC's attempts to make these changes? Perhaps you manually set some kind of non-default privilege on MC (through the compatibility settings on the application's shortcut)? Or perhaps you have more general permissions issues on the computer? In any case, I'd try a full uninstall of MC (after making a Library Backup), reboot, and then reinstall as a first step.