I have had this problem, myself. I realized that I was putting too much pressure into my arms and onto the bars. I corrected it.
You should be lightly touching the bars, theoretically, barely touching them. Your core body and legs should be balanced in the vertical center of the bike (depending on climbing or descending.) When you are roughing it downhill your arms should be jelly and relaxed. Let the bike take the beating and it will absorb most of the bumps, don't tense. When you tense it causes the fatigue (and later muscle/tendon pain); furthermore, you have less control of the bike. Practice it and be conscience of every moment feeling your body and making small corrections. An excellent book on this stuff is called Mastering Mountain Biking Skills 2nd Ed. ->
http://www.leelikesbikes.com/masteri...ls_2nd_edition