Single AA cell depletion on series battery
Your excessive pulse current battery load is killing some batteries with additional pulses on sensors probably taking more than expected.

Yes the Pulse discharge is killing the battery due to undersized requirements.  

If you notice the pulse response after 500mA, the datasheet voltage drops the 1.5V battery from  1.8V new to 1.56 but does loses 10% going back towards 1.8V each time. This is the double electric capacitor effect that takes time to restore the voltage but loses energy in the process.  THe high density doubles the capacity gives it memory effect but if overloaded you don't achieve it.  All batteries have memory inspite of what marketting has you believe. It is just the stress level and ratio of memory and long term effects that differs between chemistries.

The 3500mA rating is only for 100mA. 

While 500mA pulses plus 50?mA kills the batteries unevenly.  Series batteries must always be loaded evenly otherwise the weakest cell accelerates aging the fastest.

0'C also kills the capacity 10% (ideally) but in your case with pulse load maybe 20%.  To explain this requires modelling of the double layer effect in supercaps and batteries with unbalanced currents at low temp.

For a cutout voltage of 0.8V the rated service hours for 1.5V/cell*500mA = 750mW is 5 hours or 4 hours at 0'C and with your duty cycle of 1/60 it should have lasted 15 days. Except your Buck regulator of 4V probably becomes less efficient when the the battery approaches  1V per cell then drops from ~80% to 70% or so.

So you definitely need to rethink your battery load requirements for 4V pulsed and 3V lower pulsed with a different dual regulator solution that can withstand cold temps for same or less cost than these rare pricey batteries.

Plan on a capacity of 2 watts with a capacity of 2 months at 1/60 duty cycle or 24 Wh and expect 50% efficiency with your present regulators, temperature and pulse loading.  There are better ways , but we don't know the scope of this project.

Or figure out how to compress your power budget.