Current on Easydriver stepper pin
I just contacted the creator of the EasyDriver via e-mail and he answered me that he has heard about these symptoms and that - at least in some cases - it could be traced back to an over-voltage on this pin (likely an ESD).

The solution he advises is to either replace the IC (requires soldering skills) or to just get new EasyDrivers.

This is kind of sad, because the units still seem to work if supplied with a high enough current through the "step" pin. A possible solution might be to use transistors to switch current from the Arduino's +5V pin (or the EasyDriver's 5V output) to the step pin.