If my computer was shutting down during high usage times, I might be concerned about heat or possibly power supply problems. There could even be a memory problem, but I would check the other things first. You might check a hardware forum also.
Do you have any error indications in the Event manager?
Have you tried writing the file to hard drive first and then burning later? Make sure and shut down any non-essential programs, and perhaps even stop any internet connections you have. Nero doesn't normally shut a computer down, but something could be happening to cause it.