am no expert here, but I'm guessing you could use an undervoltage sensing IC such as the MC34164P-3 https://pdf1.alldatasheet.com/datasheet-pdf/view/12086/ONSEMI/MC34164P-3.html
Have the normal power go through a transistor, when the voltage hits 3V, have current flow through the MC34164P-3 to the circuit as well as the base of the transistor to turn it off (perhaps a PNP with an inverter between it and the MC34164P). Between the MC34164P-3 and the circuit, have something that will make the voltage climb slower. Just my probably not so great idea, hope it helps stir up some better ideas.