I have an Arduino UNO connected to four relays (3 12v LEDs and 1 12v Motor relay).
For simplicity I'm using the same 12v to Vin on the Arduinbo UNO as powers the LEDs and motor.
I've built and tested using a 120VAC to 12VDC transformer for months. It works perfectly in that arrangement. When I changed to a 12V lead battery, the system would initialize then turn off.
I measured the voltage from the transformer at 11.88 vdc, the rating is 800mA max at 12vdc.
I measured the voltage from the battery at 12.85 vdc.
My question is why is this happening and, more importantly, how do I fix it?
The voltage regulator on the Arduino may be overheating and shutting down. 12.85 V is slightly above the allowed voltage of some boards. You can reduce the input voltage using diodes (1N400x) in series with the lead from the battery to the Vin input -- each diode will drop about 0.7 V.