As a new rider (since March) I've been having the same problem. I just went back to my bike store to ask about this problem and have a proper fitting done. I was told that a lot of things were off : the handle bar stem and height, seat height, and seat position (it was too far forward). Essentially I was sitting in the wrong position and too much of my weight was too far forward. This resulted in my putting too much pressure on my hands. I haven't had a chance yet to see how much this changed things, but maybe you should take a look at your bike fit as well?