I think it's your controller. I think your controller has a LVC in it and I think your batteries are sagging so much that you hit the LVC on it.
If you aren't worried about breaking your controller (you might fry it doing this) , put 48v on the bike and then try the same hill or same route and see if that fixes your problem. 48v should put you well above the low voltage cutoff on your controller and then it won't cut out on you. You could fry the controller doing this too, though. Or your other option is to buy some batteries that don't sag as much like some lifepo4 batteries with big capacities. (this is only if I have diagnosed the problem correctly, I could be wrong but that's what it sounds like is happening to me....it's your controller).