I have two APC Back-UPS RS500 units which failed at charging the battery.
It was a capacitor which failed on both of them and I have also found out
that this failure is rather common for this UPS. Here is my description on
how to repair them. If you have a similar problem that the UPS seems to
work OK with a new and charged battery connected, but fails after a short
time (days) with the 'replace battery' light on, then this could help you.

http://www.heime.org/Lists/Posts/Post.aspx?ID=17

Stig Vidar Hovland