Is there a common approach in design to utilizing a capacitor during a voltage drop but not during a rise? I realize the cap of course must be charged at some point, but I would like immediate response on the rise. Once this rise triggers an opamp downstream, I would like to charge the cap somehow without losing my op amp reference voltage.

Thanks

 

You could use a Schottky diode between the capacitor and the load, with a resistor to the capacitor to charge it more slowly from the supply.

If the Schottky diode drop of about 0.5V is too much for your application, then you could go to a more complex ideal diode circuit.