Are you wanting a GSM module or a wi fi module.
They arnt the same thing.
In your original post you mentioned a GSM module.
Even an Arduino by itself wont run for 6 months on AA batteries,even in sleep mode as
The USB chip alone pulls around 15 ma ,which for AA batteries of 2500 maH will last around 7 days.
The GSM modules are the problem , power wise to run off AA batteries.
Heres the specs for a typical GSM Arduino shield.
Idles at 7 ma , on Transmit consumption anywhere from 300 ma up to 3000 ma.