Switch to stop battery from discharging step up
Have you considered a solid state switch?
A P-Channel MOSFET would be a good suitable choice, provided current only.flows one direction through the FET (battery only discharges).
The P-Channel MOSFET is ideal because it's is effectively a normally closed switch, when a voltage is applied to the gate then it will switch prevent battery discharge. Have a look with Google and see if this  work for your design.