Is it your watch battery or your transmitter battery?
I have a Polar FT60 and was experiencing issues with the transmitter not receiving the info, giving erratic heart rate, etc. I contacted the Polar CS (they have a real-time online chat feature which I found really convenient) and found out that I could replace the battery in the transmitter myself with a battery from any store (I got mine at CVS) but that the watch battery should be replaced by Polar itself.
Instructions for replacing the transmitter battery are available online and in the instruction manual.
The battery turned out not to be the problem with mine, though. It was the chest strap. Apparently even though I thought I was diligent in cleaning it, the sensors still got dirty enough (maybe I sweat too much, haha) that it still wouldn't receive. Rather than send the whole thing into Polar, I got a new strap off Amazon for less than $20 and voila! perfect and consistent readings again.
My only complaint is that I've never been able to get good reception when I swim laps, unless I do backstroke. But still, I love working out with my HRM otherwise and rely on it to give me an accurate reading of how much I'm actually burning, moreso than perceived exertion anyway.