I had the same with my power sounder recently. Got a used one of ebay from a 2002 car,fine for 2 weeks then same problem. I have now removed it until i win the lottery so i can buy a new one. I think the batteries must have abour 10 years life before packing up,but if you do buy new,how long has it been on a shelf? 
Just my thoughts ... with no in-depth knowledge whatsoever ......
The powersounder batteries in your car have, for 10 years, been subject to charge/discharge cycles everytime you startup/switch off the engine, they have probably had a few thousand such cycles.
The powersounder batteries in a new unit may have been on a shelf for some time, but probably not 10 years as the same units are used in other cars, but have not been subject to any charge/discharge cycles since made.
My understanding of rechargeable batteries is that they have a limited number of cycles before they fail, and if left in a charged state suffer no ill effects of prolonged storage.
A new powersounder unit is about £60 (give or take a tad).... a replacement car a thousand-ish (give or take some fairly large tads depending on numerous factors)....
When mine started "beeping" it was a simple decision .. new unit = peace of mind ... it takes as long to remove the old one as it does to remove and replace with a new one.
Look at it this way .. the cost of a new one is less than the cost of a tank of fuel.