I've been lurking in all of these TF300T random reboot threads and I wanted to post my findings. I, too, was experiencing random reboots; several times in a few hours. I had it shut down while asleep and reboot while awake and using it. This only started happening after I received the JB update, so I initially wanted to blame JB.
After reading several other users comments, I tried pressing/squeezing near the power button and could not duplicate the issue. I saw this thread and the OP's comment made me realize the one change I made other than the JB update. I had enabled auto updating for several of my apps. Before, I had none of them set to auto update and I had no reboot issues for the first month I've owned this tablet.
So, the only change I've made after experiencing random reboots is to disable auto-updating for all of my apps. So far (crosses fingers), I have yet to see another random reboot. In hind sight, I wish I would have made a list of the apps that I had enabled to auto update.
It's worth a shot if anyone else wants to try what I have. I suggest disabling a few at a time to see which one(s) may be causing the problem.
I'll be sure to post here if I do experience another random reboot.