ESP8266 disconnects after few hours
As long as I know you need at least 170mA to power the esp8266 also you need 100-200mA for the arduino and 100mA for the relay so I recommend to use a 1A power supply and solder some capacitors on the 5V and 3.3V rails. Also if your Wi-Fi is giving a ip address that is limited for certain time for example 1-2 hours you need to expand that time for your needs.If it disconnects the esp will lose its IP address and try to recover for example on my NODE MCU it works well for weeks. It also depends on your library (I am using ESP8266WiFi.h). Anyway I recommend to try the WebServer example for testing if the issue is in your code.