Automatic Capacitor Charge/Discharge Circuit
Seems like you could use just a simple Schmitt trigger which could control MOSFET's for charging and discharging like this:



simulate this circuit &ndash; Schematic created using CircuitLab
You can simulate it (Time domain 0-60s, 1s step).
Problem with this solution would be that it requires an independent power supply (You could alter the schematic to work with say 2 lithium coin cells (~6V)) for the opamp, although it shouldn't be too power consuming if you choose the right opamp (it'll leech off Ucap/16k from the cap and the rated supply current from the autonomous power supply). You could also increase both resistor values by a factor of 10, to get even less current draw from the cap, but going higher might get sketchy.
Whether it's feasible depends on your current draw though.
Hope it helps or gives material for new ideas.