what do you use as power supply? It lloks like the ESP8266 requires some 300 mA peak to work reliably.
I changed the voltage regulator on an Arduino Uno to a 3.3V 800mA one. I am powering it with a 1.5amp usb charger and/or a 9V battery.
I noticed that trying to power everything off my laptop's USB port would cause the USB port to flake out and disconnect every time the ESP8266 tried to transmit (!?) The OS didn't report an overcurrent condition like I know it will if you short it, but it seemed like that was the issue. I'm thinking a big cap would have smoothed it out.