Nanny
This script tracks the "error log" from qtminer and looks for patterns that suggests that the mining has stopped. If found, the computer is rebooted. In order for this to work, the stderr of qtminer has to be set to ~/nanny/error.
$ qtminer -<your usual options> 2> ~/nanny/error
Make sure that /sbin/reboot doesn't require sudo:
$ sudo chmod u+s /sbin/reboot
Don't forget set this script to start-on-boot