I am assuming you are talking about a UPS.
Chances are, you have a decent PSU that has active PFC. It doesn't like the modified sine wave the UPS provides, and shuts off. If that is the case, you will need a UPS that provides a true sine wave, like the APC Smartpower series. They are more expensive, but will solve this problem.
Edit: If, on the other hand, you're talking about a laptop, how old is it? The battery may have reached the end of its useful life, and need to be replaced.