Capacitors not keeping charge as expected
I don't see anything dynamic here. No positive feedback, no bistable circuit. 

There is no AC input (except maybe ripple at R1, where it does no good). There is no transistor switching. The transistors Q1 and Q2 are assembled as a two stage amplifier, rather than as a bistable oscillator - why? Perhaps R6 should be tied only to R7 and C2...

There are no rectifier diodes, which I expect to find among  doubling capacitors. Perhaps R7 should be replaced with a diode?

The two transistors Q3 and Q4, below the LED, are connected in parallel - which is a distracting complication, rather than a true example of a LED constant current sink. Although biased (as shown) by a constant 2VDC supply so the base current is constant, this pair will not limit LED current using feedback. Perhaps if Q3's base was tied to the others emitter, and Q3's collector was tied to the others base...