I've never had "flat" fresh ginger. Seems to me when it gets too old it basically becomes dried up, hard and nearly impossible to cut or grate (which you can see even before you take a knife to it).
I keep my fresh ginger in the freezer. It does change the texture a tiny bit, but it doesn't seem any effect on the taste; it still delivers that distinctive bite and flavor. It's much easier to chop with a knife when it's frozen -- though it is harder to grate on a mico-grater 'cuz your fingers get so cold holding it.