What do you mean that the PS is shutting when supply goes ? The UPS is designed to give a small amount of time in a power loss to properly save and close your work. Most lower and medium priced UPS will give you 5 min depending on what you have plugged in to it.
i think he means that when the power goes off the battery backup is not providing power to the system.
this makes me think of two scenarios:
-the ups has an issue with either charging the batteries or switching out to battery power when the power goes out.
-your system draws too much power for the backup to handle.
i have a $250 apc battery backup hooked up to an i7 gtx470 system and i get less than 6 minutes of time at a draw rate of approximately 330w. if you have a cheaper unit it is highly likely that you exceed the limits of the battery backup.