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Does it turn off, or simply enter sleep mode? If so, you can change when it sleeps by choosing Settings -> Auto-Lock -> and select a time. Hope this helps.
There may be a break in the heating element inside the toaster. If your outer casing can be easily removed, you can find where the wire may be broken. In order to fix it, you can either replace the heating element or attempt to repair it. Since it gets very hot, solder may melt, so instead I would recommend simple wrapping both broken ends in a short single length of bare copper wire. Make sure the wire does not touch the outer casing or bread cages. Good luck, be safe.