How to keep the state of relay
You can realize the required function using a diode. What needs to be done is to pull one of the inputs of the opamp to such a voltage that the opamp's output stays high (and the relay powered).

Add a diode (1N4148) with the anode to the opamp's output and the kathode to the + input of the opamp. Then when the opamp's output is high (and the relay is powered) the + input of the opamp will be pulled to a higher voltage than R3 and R7 supply (which is about 6 V). The - input of the opamp will not be able to reach that voltage (it will always be at a lower voltage) So the output of the opamp remains high.

To add the reset function, add a 1 kohm resistor in series with the diode and add a switch to ground from the + input to force it low so that the output of the opamp becomes low as well:







simulate this circuit &ndash; Schematic created using CircuitLab