I use Glycerin to recondition my stamps. When I notice stamp rubber turning white or looking kind of dry I rub glycerin on it. I let it sit a couple of days to absorb and if it is still dry add a TINY bit of glycerin, rub and let sit.
Note: I contacted a stamp maker and asked about stamp rubber turning white or pale looking without being dried out. She said companies use to make their stamps out of a certain rubber but most have changed to the red kind.