The XBOX wireless controllers do indeed work when I put the XBOX in the closet. Thanks for all the useful advice, including those links to other people who had the same problem on avsforum.
I also have an XBOX "remote control" to control DVD content, and strangely, this device is completely line-of-sight and does not work with the XBOX in the closet.
I guess I expect a regular ol' remote control to *require* line-of-sight, but what surprised me was that the XBOX appears to have BOTH types of sensors: RF for the wireless controllers, and that little IR sensor on the front for the XBOX remote control. I figured they would just build in one or the other.
For the XBOX remote control, I think I'm going to have to work out some type of RF reflection/extension capability. Any thoughts or confirmations of this or stories of your own successes are greatly appreciated.