Could you use a variable resistor to adjust the voltage to a relay? While the relay is closed, the circuit works, but when the voltage goes below 4.6v, the relay switches off and the circuit opens. Use the variable resistor to adjust at what voltage the relay turns off.
Use your meter and a varible resistor (different one that you remove later) to adjust the voltage to 4.6v. Make sure the circuit is on then turn the variable resistor for the relay slowly till it switches off, then turn it back so its on. Remove the second veriable resistor and connect back to main power. When the voltage goes below 4.6, the relay should shut off.
~Mike