I have had some equipment, sat receivers mostly, act like that. Sometimes an extended time without power will bring some electronics back after the circuitry has completely discharged. That could take overnight due to the way capacitors hold power. If not, then might need repaired. Satellite receivers I have had over the years have done that and it always seems to be bad capacitors. Replacing them is the only option.
First I would try no internet connection and see if it stays on. I would Try different cable to TV. I would check anything that could cause a short to rule out an outside influence causing the box to shut down. Even the possibility of unstable power at an outlet by plugging in alone on a different circuit. If you can get into the BIOS, go there and leave set. See if box stays on in the bios. These are just things I would do to try and diagnose the problem. Luck to you! Have a great day!