The best thing to do, is to try to think how you are using your arms when riding. Really focus on relaxing, and not gripping the handlebars to tight. That's usually the biggest reason for this. I have noticed that the more excited or nervous I am, and the tighter the race is, the more tired I get in my forearms. This is because I tense up, and try to force the bike into every corner, and really wrestle the bike around.
Also, check that your leathers aren't too tight around your forearms. This will obstruct the bloodflow, and make the forearms really cramp up.
I've been having some problems with this when racing for some time now, and apart from practising on your bike every day, there are a couple of good exercises for the forearms that I use.
1) I use a kind of gyro-ball that I bought at a gadget store, works great. It's a bit tricky at the beginning, but when you get it right, its really good exersise.
2) Take a short pole (cut off a broomstick or something). Attach a string (about 3-4 ft.) to the middle of the stick, and then a weight at the end of the string. (Try different weights, until you find the right one).
Then grip the short pole with both hands, arms straight forward, and wind up the weight all the way up, and then back down. Do this both with the knuckles facing up, and facing down (works different parts of your forearm).
3) Use the classic "squeese-spring-thingy". (Have no idea what they are called) You know, the one that looks like a set of pliars or something, and a spring inbetween.
Edit, found a pic.
Try to work with lighter weights and a lot of reps, rather than heavy weights and fewer reps. This will increase your muscle stamina, and not build volume. (Don't want the leathers to get to tight around your forearms)