This problem is very often closely linked to the way you ride, and in particular the way you use your body, hands and feet on descents and when braking.
One of the skills we work on a lot is footwork and using your lower body to absorb more of the trail forces so your grip can be lighter and your bike control can then become more confident and relaxed at the same time.
In addition a common cause of pain is from riding with brake levers too close to grips, which forces you to seat your hand partly on the corner of the grips overhanging the edge, rather than squarely in the centre of the grip (with a bit of bar sticking out to the side). This is even worse if you use metal-ended lock on grips. Instead of the fatty pad of your palm being on the bars your nerves are placed under far greater direct pressure.
If you want more advice on this or the links to a couple of features we have written on footwork then feel free to fire me an email on chris@cycleactive.co.uk and I'll gladly fire them over or send you some links.
Cheers
Chris@CycleActive