I would recommend putting the device into safe mode (if applicable). If it reboots while the user is in safe mode, then it is going to be a larger issue and would need to be replaced. If it does not have an issue while the user is in safe mode, then it may be a downloaded application that is causing the issue (ex. task killer, virus protection program).
Just thought I'd post my 2 cents here on this topic. I have had my X for a month now ... Love it. I've had like 2 or 3 on-its-own reboots. The only thing I can put my finger on is it has to do with when I have GPS turned on and doing "location/place" type of information gathering. I installed an app over the weekend (My Location Widget) so that I cold post my location for friends at a fair I attended. I also had the FaceBook "places" thing active ... I had Twitter up and live, all this GPS stuff going in the background, etc. and in the middle of the street fair it rebooted. So I'm not sure, but it SEEMS like either GPS type of activity caused it; or just maybe I was running way too much applications for it to handle. (I do NOT run ATK.)
Anyway, there just seems to be some limits with how much and WHAT can run on this device... Otherwise it's been rock steady and it stays up all day long until I shut it down at bedtime. YMMV.