Tried the HDMI CEC/control settings? Certainly sounds like that, although not sure if you'd need to disable it on the tv or 360, or both.
X360, HDMI and HDTV throws up all sort of weird problems.
I got my X360 connected to Sony 42" HDTV via HDMI for years, then last month had to move around the basement office/game room stuff for minor re-decoration, then put everything back.
Only now when I switches my TV to TV or other AV, my X360 switches itself off, including when putting X360 on pause and put TV on standby. Same problem.
Frustrating as cant dare put TV over to PS3, PC or whatever away from X360 and tried everything, changing back settings switches off HDMI control on TV and so on. I got no other AV or audio leads to TV other than single damned HDMI. Switches to different HDMI no joy.
Why now? Why resets X360?
Changing resolution, changing display discovery, changing all kind of settings on Sony Bravia TV. No result but same problems!
I ll keep looking for solutions, and will report back if find anything that works other than getting new TV or X360!