Keep relay energized longer with capacitor
You need a capacitor on the watchdog power supply, otherwise the relay will cut power to itself before being fully operated and its contacts will rapidly fall back to the NC (Normally Closed) position. 

The Pi normally draws a lot of current which you don't want taken out of the capacitor, so you also need an isolating diode. A Schottky diode should have low enough voltage drop to allow the use of a 5V relay.   







simulate this circuit &ndash; Schematic created using CircuitLab

The release voltage of a relay is usually much lower than its operate voltage, due to the smaller air gap and resulting stronger attraction of the armature to the core when operated. So provided the capacitor can hold its voltage up long enough to fully operate the relay, it should be able to keep it operated for a significantly longer time. 

A typical 5V relay with 5A contacts might have a 50&ohm; coil, 6ms operate time and &lt;1V release voltage. The formula for capacitance is C=I*t/V. So if you needed eg. 6ms with 0.5V drop (4.7V to 4.2V) at 90mA, the required capacitance would be 0.09*0.006/0.5 = 1080uF. As a capacitor discharges the current and voltage reduces exponentially, so the time to reach 1V would be much longer.      

Hopefully the 555 will keep the relay operated until the capacitor has discharged to a low voltage. If not then the flyback diode (D2) should slow the relay's release time by recirculating current through the coil. 

To ensure that the Pi's supply voltage goes down to zero rapidly you could also wire a low value resistor from the relay's NO (Normally Open) contact to ground.

As an alternative to a mechanical relay you could use a Solid State Relay or MOSFET. These options would have much lower holding current so the capacitor could be made much smaller, and they should be more reliable. You might also consider keeping the watchdog circuit powered continuously and pulsing the relay, as this would solve the problem of how to hold the voltage up long enough to do a proper reset.