My dear old generation 2 Kindle is not holding a charge for more than three days and I wondered if a battery might be its problem.  It has certainly been used well and I have really enjoyed it and will replace it sooner if the battery doesn't work. Some advice please.......

I suppose that could be the issue.  contact Amazon and ask them about it

All the batteries in eReaders are lithium-Ion IIRC, and they have a certain amount of recharge cycles before they start to lose charge. It all depends on how old it is, how many full charges it's had, how hot it's got and how often it's used.

I think I've seen 2 1/2 as an average when people see their batteries go down and won't recharge much. 

Here.

• Lithium-ion batteries age. They only last two to three years, even if they are sitting on a shelf unused. So do not "avoid using" the battery with the thought that the battery pack will last five years. It won't. Also, if you are buying a new battery pack, you want to make sure it really is new. If it has been sitting on a shelf in the store for a year, it won't last very long. Manufacturing dates are important.

Which is something to keep in mind when buying used items with lithium batteries, and why the price drops drastically when they get older. One store I go to that takes electronics, games and books for trade-in won't take eReaders if they're over a certain age because they have to assume the battery is about gone. And it usually pretty expensive to replace them. I tried a self-replacement on an older reader I wanted to keep. I spent $25 on a replacement battery and changing it out was easy, but the new battery only lasted a couple of months. (probably a cheap battery for a reason!) I ended up getting a new reader anyway.

Here's part of a post from the Mobliereads forum about battery charging:

AT LEAST ONCE A MONTH go through the following procedure. (This, by the way is identical to the advice Apple provides for the iPad. It works for any lithium ion or lithium polymer powered device.)

() Turn off the KF. (If it already appears to be dead, you can skip this step.) "Turning it off" means holding the power button until the message appears asking if you want to turn it off. Say yes.

() Plug in the charge cable from Amazon and let it charge for at least four hours, preferably overnight. Pay no attention to the orange or green light. Don't turn on the KF to check on progress. LEAVE IT ALONE. Use the Amazon cable unless you are ABSOLUTELY SURE that the cable you're using supplies at least the same amperage as that cable, about 2 amps. Do NOT use cables that charge more slowly. They won't hurt your battery but they may well throw off the synchronization with the battery monitor.

() Unplug the KF and boot it. Use it normally until you see the 15% battery remaining warning. At that point, shut it down again. Do NOT allow the battery to discharge completely. It probably won't hurt the KF or the battery but it does shorten the battery life if done repeatedly. (The software should shut down the device with about 5% charge remaining but why take a chance.)

() Repeat the charging process above.