not sure if this will help you or not, but I had a problem with my one repeatedly turning itself on and off earlier this year. It was not random but a continuous cycling on and off which apoears to be different from what you're seeing. however, the following fixed my problem
open wordpad and save the blank document as "poweroff.txt"
then open a file manager and rename the file "poweroff" removing the .txt file extension
load this file into the root directory of the tomtom and see if it makes any difference. if it does not, then you can simply remove the file.