Why doesn't this oscillator circuit work?
Q3 will work upside down; the hFE will be low but it will still work as a transistor (it will actually saturate at a lower voltage but that is besides the point). 

Why doesn't this work? Or better still why do relaxation oscillators work - the simple answer is hysteresis. Your circuit has no hysteresis therefore it operates in a linear fashion and finds a perfectly likable equilibrium with about 0.7 volts across R2.

What would have been preferred is for Q3 to act like a trigger - once activated it stays activated until the voltage across C1/R2 has dropped (maybe) to 50%. Then the whole process will start again with C1 rapidly charging then triggering Q2 which then discharges C1/R2 thus an oscillator is created. Remember that Q3 can work upside down and the base-collector region is the new base-emitter region.

Sorry, it won't happen like that in a linear circuit - it just finds a nice equilibrium and sits there. Relation oscillators need hysteresis! Here's the archetypal op-amp relation oscillator: -



R3 and R2 provide positive feedback and this creates hysteresis. Here's a useful oscillator to try: -



It's called an astable multivibrator but if you want some other options hit this link.