Never heard anything near that. If there were battery problems we would have heard about it by now and it would be very expensive for Apple as the Nano would be covered by a 1 year warranty. I doubt apple would want to replace a the battery on every Nano every few months.
Possibly every 3 years or so like other rechargeable batteries, which eventually die. But as others have said, there have been no complaints (yet, but give it time, someone will complain eventually) about battery problems with the iPod nano. I've found that I actually get better than advertised battery life out of my nano. The same is not true for my old 4G (may it rest in peace).
The stories you have been hearing are complete and utter tripe and should be disregarded as quickly as possible.
iPods suffering battery issues haven't been sold on the market now for nearly 2 years but for some reason people seem to latch onto an old issue and try to keep it current just to give themselves some backlash material against the market leader.
The nano is one of the most stunning and durable (it might scratch up a bit though so get a protective case or film) products Apple has made. If I weren't saving for a 5G iPod I would've snapped up the nano in an instant.