Qdeathstar:
Yep, i've found that you need a powersupply capable for providing about 2A to get reliability from an esp8266. Im sure with a better design, you can get closer to the 500ma it states in the "data sheet" but i got to piss with the cock i got...
My concern is with Amp-hrs rather than amps. I need to run off a 160mAh LiPo which also drives a small DC motor.
The ESP8266 works fine off a pair of AA alkaline cells that are well past their best. I have not actually tried it on the LiPo because I would have needed to reduce the voltage a little and I was lazy.
...R