Here's what you need to do:

First, go to a good, REAL bike store, and buy some DECENT tubes (not the cheap Kenda or the junk they sell in the dime stores).

Second, you need to buy some good, puncture-resistant tires. They'll cost you about $40 each, but they are worth it.

Third, if you have rubber spoke liners, you need to replace it with a good cloth liner.