If your batteries have Battery Management (monitoring?) System, BMS, it could be that circuit is killing the power to protect the batteries from an excessively high discharge current. If that's the case then, strange as it seems, a higher AH pack may solve the problem as it's BMS will allow proportionally more discharge current before cutting off power, maybe enough to get you up and over the hill.

16AH should allow for a 60% higher current than 10Ah.

Let me cover my you-know-what by saying while I have a decent grasp of electricity, I know enough about batteries to be dangerous