I have tried all the suggestions but those did not solve the problem.
After some testing (with A, D and S turned down), I saw that the voltage at pin 2 of the 555 showed some weird behaviour. My expectation was that it remains high at all times, with short spike down to 0V when the gate goes high. However, after this spike down it remained around 3.4V until the gate goes low again. When I disconnected pin 4 of the 555 this behaviour ceased. It seems that the reset pin of the 555 forces the voltage to go down. Having a lower voltage at pin 2 will certainly mess with the workings of the circuit and basically prevent the decay-phase from starting because the 555 is not reset.
So I put a diode at pin 4 to ensure that all the input circuitry is operating nicely without interference from the 555. I really don’t know why this is happening but now I finally have some snappy Attack-decay envelopes.
This is what the schematic looks like now:
