mah refers to miliamphour and is the capacity of the battery and not directly current. current is voltage divided by resistance.
The problem is your 1600 mah battery probably has a couple of bad cells or something and is outputing a low voltage and thus current would also be low(not enugh to pull spring). nickel anythings (cadmium, metal hydride, copper\zinc etc.) ability to output stated voltage diminishes quickely(aa or aaa only output 1.2v) unlike alkaline or lithium batteries. older ni** batteries will be even worse.