Wow that's pretty crazily bad. Maybe try restoring it in iTunes, see if it squashes any bugs. Either that or you may have a defect device that's overheating or something. I've had mine plugged in for weeks, with standby disabled and it's not had a single issue. So it should be stable.
The other possibility is that an app could be causing it. Is it always when you are using a particular app, or just random.