Behaviour of capacitor discharging through a transistor's base
Your analysis is flawed. If there was a 220ohm discharge process this would also be present when charging BUT clearly this isn't the case by your own acceptance of what is going on. You said: -


  This works as expected.


When you open circuit the switch there is a very weak (by comparison) discharge of C1 by the 220 ohm multiplied by the hFE of the transistor so, 220 ohm becomes more like 22k or much greater (transistor dependent).

If you want it to discharge at approximately the same rate try using a 2 position switch where one position connects to a 10k pull-up resistor (as per your circuit) and the other position connects to a 10k pull down resistor.