555 timing capacitor discharge via threshold input
First I must say... YUCK.

When you close the switch it powers the 555 which in turn drives its output high, pulling in the relay to keep itself powered when you let go the button.

After the timeout the relay is released.

As you have discovered there is no actual discharge path for the capacitor. In reality what will happen is the capacitor will discharge through the power pin of the 555. Mostly through the three resistors that setup the reference levels, plus whatever quiescent current the 555 still draws with that voltage division.



That of course will result in a decay time longer than your set on-time. So the next time you trigger the circuit the delay will be significantly less if the cap has not had time to reach zero volts.

You can correct that a little by adding a low resistance discharge path, D2 and R3 down through the relay coil as shown below. I included D3 so the inductance of relay coil current does not pull a negative charge on the cap. Note: Using the discharge pin may not work, since the 555 is unpowered, the state of the discharge transistor is undefined.







simulate this circuit &ndash; Schematic created using CircuitLab

You will still have a slight variation on second firing due to the diode drops though. Using shotky diodes would help, but watch out for the leakage currents on those.