I had the same problem and Xbox Support did not help at all. They kept sending me to general trouble shooting links despite the fact that I had described my issue to them in detail.
First go to System Settings under My Xbox.
Choose Console Settings.
Choose Remote Control. - There are 2 choices: Both Remotes and Xbox 360 Media Remote. (My Xbox already had Both Remotes selected, but I chose it again anyway because of what meanchase said above.)
Choose Both Remotes!!
Instantly it worked for me, I did not have to restart the console.
Thanks meanchase for helping me figure it out! I was so frustrated. I've never had such a ridiculous issue like this before. That's a FAIL Microsoft.
I've seen that the XBOX 360 Media remote has similar learning functions, allowing me to stick to my current single remote setup, and keep it as simple as possible for my wife.