Its been pretty cold of late, was the bedroom you left it in heated? Could be that it got a little cold/damp while switched off and needs to warm up slowly before use.
I know that if you have a new SKy+box installed, the Skyman advises that they are left on Standby for a few hours to aclimatise before constantly switching channels etc because the boxes have been stored in a cold warehouse for quite sometime.
It would be interesting to see if it "stops" at the same time for the same length of time each night, could be just the digital clock screen is broken if the rest of it appears to work ok and it records ok. I gather the DTR doesn't have its own freeview card and user guide, because if you set the record for the program from the guide, the recording is initiated by codes sent out by the program rather than time, which is why you also always get a few minutes before and end of a programe. Try testing by recording a very early morning programe, if the box does actually lose power then it wont record. Personally I think that if it turns itself off, it would stay off!
Have you tried unplugging the DTR and moving to another room, ie plugging it into your living room setup to test its not the aerial connection playing up or sockets. If it loses a few hours overnight it sounds more like a software gliche or poor connection than a hardware error. I would also go along with Bigcol and see if there is a firmware update, though as we don't know the model, I'm not sure if your particular DTR can connect to the internet or has a USB port, depends on the age.
Jenny