Six months is about the limit for Fully Charged batteries with no load. If there is any kind of load at all.. That goes down, And in this case swiftly..
A pair of GC-2 Like the T-105 has a capacity of about 220 amp hours. Let's use that figure (might be 10 more or less) But let's take 220.
OK, how much power does the Propane detector draw? I picked one at random 108mA (0.108 Amp) so every hour it's taking about 1/10 amp hour. or 2.4 amp hours per day. You have 220 Amp hours (At the 20 hour rate, A bit more at the sixth month rate).
that's so 100 days is 240 amp hours... Six months is 180 days.. Nearly twice the capacity of the battery.. JUST FOR THAT ONE DEVICE.