While it is easy to get it overly complex a simple motor starter or DPDT relay is the circuit you want, the momentary power drop out will be a big annoyance. A solution is to put a UPS or equivalent on the relay circuit. Doing so means the UPS like, device only needs to have sufficient energy storage to power the relay. The coal appliance will stop working during the power interruption, but the relay will stay in the on position for as long as the UPS has power storage.
For example you could use one of the many electronic junk DC "wall warts" you have laying around. With an relay having the matching coil voltage, you wire one pair of the DPDT contracts to power the coal appliance. The other set of contacts is wired as your drop out circuit control. The drop out time delay is now set by how long it takes the "wall wart" DC output to discharge below the relay coil hold-in voltage. A tinkers delight solution to a common problem.