The watch batteries don't have the capacity to power all the electronics. The GPS pulls about 25ma under acquire dropping to about 5ma once it gets into power saving mode. The only battery we recommend people use for this are the Energizer Ultimate Lithium's which are 1200mAH for the AAA and 3000mAH for the AA's and are known to work below -40'C. The watch battery is 24mAH so you can see the issue :)
For the record the tracker uses about 40-45mAH which is low, there are some inefficiencies in the step up convertor. The hardware in theory can squeeze more out of the battery as I can switch the GPS off entirely from the microcontroller but I've not coded this yet.
For this flight the 7.6g AAA will be fine gives over 26 hours. For the record nothing touches the L91 and L92 Energizer Lithiums for the weight vs capacity.