The weak point in the Humax is the power supply. I've had to replace mine twice. So it may well be something to do with that, as you suspect.
I would have thought that it was unlikely, but not impossible, that it was a software fault.
Another possibility is a power surge/ spike originating from your mains power supply. Try taking the Humax to a different location and connecting it to the mains power. You don't need to connect it to anything else, just watch the LED display at the front of the box to see if it is re-booting.
If the problem disappears, you can then invest in a surge protector to solve the problem. Obviously, do the test before forking out the money.