More info would be needed on the motherboard, operating system and general system setup to give a good answer, but I'm guessing the system probably shuts down because of heat or power supply issues? If so you might be able to set the BIOS to automatically start after a power loss and use something like this product to power cycle it from a remote location:
http://www.audon.co.uk/ip9258.htmlOf course the better option would be to find the real cause so it isn't necessary.