Aha! On some systems, you'll find the power on resume won't work if the system has been shutdown properly.

I had this problem with a linux box, the power would go off and the box would shut down gracefully. Once the power returned the UPS would go back to mains and power would return to the box. Sadly it then required a press of the power button.

The solution, don't let the UPS shut the machine down. Just run it off the UPS until its exhausted and cops out. Once the power comes back the machine starts up. The box in question runs a journalled file system so doesn't mind the power being pulled.