All of the Vcc ports on the Arduino come from the same regulator. So connecting a second Arduino Vcc pin to the relay board will not help.
If everything is shutting down then I would have to think the regulator is shutting down. Will it run longer if the relay board is not connected?
I would begin to look at obtaining an external 5V power supply to connect to the JD-VCC (with the jumper removed). Don't forget to connect the ground of the second power supply to the Arduino ground.