ZiggyFlavel,
Battery weakening does not happen quickly.
Every time you recharge a battery it loses a very very very small amount of it's holding capacity. So if your battery runs for 5 hours on a full charge when new in 12 months time it will only hold enough charge to run for 4 hours. In 2 years 2 hours until eventually it will not hold a charge at all, this is normal.
With Lithium Polymer batteries if you always fully discharge the battery and then fully recharge it all the time you stress the battery and speed up the process and your battery will lose power quicker so for instance if you can expect 2 years reasonable use from your battery you may only get 18 months. If you recharge often and do top ups the battery is stressed less and you will get the maximun life from it.
At the moment if you let your player charge for 4-5 hours set your LCD to turn off at 10sec, how long can you play music for till your battery is flat?
I noticed that there are new batteries for nano clones on eBay
here but you would have to solder it on to your player as unlike the Nano it does not have a connector