Sorry to say, but Retro Grouch is 100% correct. What's going on is that spokes all have a "life expectancy", if you will. The more you ride them, the "older" they get. Once their time is up, they break. Better built wheels use a few different techniques to give their spokes longer "life expectancies". The best wheels end up being retired not because they start breaking spokes, but because the brakes have worn down the rims so much that they're too thin to ride safely. Rear wheels break spokes much more often than front wheels because there is more weight being carried by the rear wheel.
Anyway, if this bike is worth anything to you, I'd go down to your local bike shop (LBS) and see what they recommend as a durable, reliable wheel. You could have your wheel rebuilt with new spokes, but if the bike was fairly inexpensive to begin with, it would probably be more cost effective to just shell out for a new wheel.
It is my belief that every person in this world has something to teach, and everything to learn.
In memory of Jim Price (aka. sydney) ...