I think someone here also suggested using hair bands (i.e. soft rubber bands) to hold door handles together and keep them closed. Maybe small pet collars (i.e. straps with clip-closures) would work, too?
We haven't had that problem - except when we had to stop short one day, and the heavy pots were able to push open the cabinet doors from the inside... luckily, we keep the heavy stuff at floor level, so no damage was done - just a small mess of putting stuff away again.