Heavier spokes aren't necessarily the answer. Where are the spokes breaking? What kind of wheel / spoke / hub are you using? If they are breaking at the elbow that hooks into the hub then it is more likely that improper tension is the culprit.
There are as many causes of spokes breaking as there are spokes in the wheel. More information will bring out many informed opinions from BikeForum members.
__________________
2003 Iceman Challenge - 2:34:55 - 897 / 2,000*
2002 Iceman Challenge - 2:39:23 - 1093 / 2,186
2000 Iceman Challenge - 2:49:18 - 1516 / 2,153
*estimated