I have a ESP8266 wifi module connected to an arduino uno. On the ESP8266 I set up a socket server witch is working fine. And I can communicate with it as I expect.
After having run the ESP8266 some time (like 5-10 minutes) it automatically turns off (or goes into some kind of sleep mode. The LED turns off). I then have to re power the whole thing and reset it using the reset pin.
Why is my ESP8266 turning off and disconnecting from the WIFI?
Maximum current draw from this voltage regulator on the Arduino Uno is 50 mA. It's surely not enough for ESP8266.
You need a power supply with at least 700 mA to make sure it works properly (ESP8266 usually takes about 60 mA but according to my experience the current draw can be very high during the startup).