The MCE remote toggles remotes between 2 codes for each button. As most learning remotes cannot learn 2 codes for a button this feature needs to be disabled. This can be done by editing a registry setting in Windows XP.
The key is called EnableDebounce, it's found in the following location:
So, fire up RegEdit, navigate to the appropriate key, and change the EnableDebounce value from 1 (its default setting) to 0.
Note: You'll have to reboot your system for this change to take effect. After this modification, the single code sent by the learning remote will work correctly.