Some recipes for mazta have chemical leavening. Chemical leaveners operate very differently at varied elevations. See here for conversion and tips. This is a very common problem. Judging by the problem, it seems like you were previously closer to sea level and this recipe worked fine. Am I right?
Basically [no pun intended], baking powder is a mixture of desiccant, baking soda, and cream of tartar. When water mixes to make a solution, the chemical reaction ensues releasing CO2 gas as a byproduct of soda bicarbonate and cream of tartar (an acid).
Higher elevation causes this reaction to carry out much faster, and this is how your balls are blowing apart. The solution [no pun intended] is to make a stronger dough with more flour, more kneading, and more powder so that the rise is slower, more controlled, and better tolerated by the ball.
Heat also causes the reaction to take place faster. It may be annoying, but try pulling the soup off to cool for a bit, then bring it slowly back up to temperature.