I have two of these units with the same fault and I have also read about this problem on usenet. The problem is that the Back-UPS RS 500 stop charging the battery. For me it was easy and not expensive to repair them. If you have some experience with soldering it should be easy for you too to do the repair work.
Before you start, remove mains power and the battery. This unit is generating high voltage from a 12 volts battery and a battery like this contain a lot of energy. Please take notice of any safety precautions.
Here is the front panel with model name. I suppose yours are similar.
Remove the two screws on the back panel
Lift the panel out at the bottom. It snaps in position at the top and you maybe have to use some force to take it off completely.
Lift out the side panel and disconnect the red and black battery wire. Make sure you know where to reconnect those wires when assembling the unit.
Take a sheet of paper and make a drawing of the circuit board and all the wires to the transformer and back panel. Disconnect all the wires and remove both the transformer and back panel.
Remove the circuit board on the front panel.
Remove the main board. It is fastened with two clips on the back side.
Main board with the faulty capacitor.
Charging unit and the faulty capacitor.
Make sure you take notice of the polarity of this capacitor.
Replace the capacitor with a new one with similar or better specification. I bought mine from here: Elfa
After the unit is assembled, connect it to the mains and measure the voltage at the battery terminals without a battery connected. It should be approx. 13.6 Volts.
Disconnect from the mains and mount and connect the battery. You probably have to buy a new battery if the old one has been completely discharged and been like that for several weeks. Batteries are easily damaged if discharged over a long time. Connect it to the mains and measure that it is charging the battery. The voltage should be rising slowly up to 13.6 Volts.