Even if the motor is drawing 2 amps at start up the 754410 chip (if that's what the board is using, and it's possible) is rated for 2 amps peak (for 5 milliseconds, which is usually long enough for most any onrush spike).
Since I doubt it's a matter of the Pololu product being badly designed
-- it's just off the shelf parts -- it's possible that A) you happened to get two bad boards, B) somehow you are smoking the boards doing whatever, or C) there's something screwy about the motors. IOW, it has to be *something*.
Mitch's suggestion of a honking resistor to simulate the load of the motor is an excellent one. Since this problem may reoccur with your own design that also uses off-the-shelf parts, it would be helpful to eliminate any possible issues by narrowing the field of suspects. Consider is a form of forensics for electronics.
-- Gordon Author: Robot Builder's Bonanza Budget Robotics: