The cause of this problem is that the internal battery is dry. This doesn't automatically mean that you have a fake; the battery could have simply just run out. If you have a G/S/C game from back when they were released, then you'd be experiencing the same problem.
I'm not sure how long batteries are supposed to last, but I heard that it was around 7 years (for the G/S/C games, that is). If your game has run out of battery before approx. 7 years, then it's just a dodgy battery. In this case scenario, all you can do is buy a new game. Nintendo doesn't replace batteries simply because you'd probably end up paying them more then buying a whole new cartridge.
And never buy games off eBay, as you will often get fakes. These 'fakes' can be identical to real games to the naked eye, so just because they 'look' genuine doesn't mean they are.