It would be surprising to see Flash memory fail at this point (number of write cycles wise it would be impressive if you got it at launch, played it all the time and saved every second for it to have gone at this point) but it is not impossible -- things randomly die all the time.
I will note that this was one of the titles to come with the pokewalker and I don't know how reliable that selector chip is, bonus though if it is that then you can bypass it (at the cost of the pokewalker) -- before the various save dumping tools were remade to account for this then people took to bypassing the selection chip with a wire, will have to search for one of those threads to cover what would need doing.
Before going down those paths I assume other games save OK. Also that you have tried cleaning the pins of the cart. If you can then trying to save in another device would be nice to test.