I also have a problem with a mast head amp where we can no longer access it, next door built a garage where we would have put ladder, I have had aerial fitter around with his box, which showed great signal, but within a short time of him leaving the TV again failed, I went into TV menu and set TV to output power instead of using the power supply, this seemed to work fine.
When the TV was replaced found new one did not have output to aerial so bought a new power supply. Started to get problems again, both with old and new power supply, I removed the aerial wall plate and connected direct, same results what ever I do works for so long then fails, I have noted the power supplies are 12 volt, but the TV output was 5 volt, it does seem with the 12 volt something is failing after some time, but with 5 volt it just runs and runs. I will guess there is a fault with the mast head amplifier and something is over heating in it?
I have given up and had a satellite dish fitted on the wall low enough that I can reach from a set of steps, I have given up with freeview as also other issues with the TV asking to be re-tuned every couple of days. However since my mast head amplifier seems to work better from the 5 volt output of TV than the 12 volt power supply, maybe yours will be the same?
Before living with my mother it was really a pain, as soon as power removed and re-instated the mast head amp would work, so seemed impossible to find the fault. Could even be a little water in the amp and it stays as water with 5 volt but becomes a saturated mist inside the box at 12 volt, but what ever was happening it worked on 5 volt 24/7 but not on 12 volt which was the voltage of the original power supply that was supplied with the mast.