Not totally sure about the ESP8266. I used a WiFly RN131 in a sensor product that woke up every 15 minutes and sent a reading. AA batteries lasted probably 18 months.
Biggest problem we found was enterprise networks would randomly kick you off if you were using DHCP. I think because they would assume that if you hadn't transmitted in five to ten minutes it meant you'd gone away. Using static IP fixed that.
Edit: Friend of mine that mucks with ESP8266's uses the low power timer to reset and wake the device up out of deep sleep. (Via a simple hack I think just connecting a timer pin to the reset).
Biggest problem we found was enterprise networks would randomly kick you off if you were using DHCP. I think because they would assume that if you hadn't transmitted in five to ten minutes it meant you'd gone away. Using static IP fixed that.
Edit: Friend of mine that mucks with ESP8266's uses the low power timer to reset and wake the device up out of deep sleep. (Via a simple hack I think just connecting a timer pin to the reset).