I’m not sure how all of your numbers work… 15 minute duty cycle… on or off? I’m guessing off… 8 seconds to wake up, is that the total ON time? If so, and we assume worst case power draw of 300mA.
Avg Current Usage = 300mA x 8/(15 x 60) = 2.66mA
14000mA / 2.66mA = 5263 hours (219 days)
That said, AA NiMH batteries are notorious for self discharging… so I would give your batteries 7 days before they are dead, a month or two if you are really lucky with some good cells.
Best low self discharge common cells out there really are Alkaline batteries … but as far as rechargeables go, Lead acid and then Lithium Ion/Polymer are your best bet.