Why does adding a capacitor greatly improve this circuit?
simulate this circuit &ndash; Schematic created using CircuitLab

Figure 1. OP's circuit adjusted for ease of reading.

It is not clear how you expect this circuit to work. The combination of R1, R2 and R3 looks like it is intended to apply some positive feedback to make the circuit operate as a Schmitt trigger.

You might be just getting lucky and somehow switching on the NMOS / PMOS output, causing the V+ to drop and that drop is getting "kicked" through the capacitor enough to switch the comparator and get the circuit to oscillate.

Overall, I'd recommend that you edit your question to explain how you intend this to work, add in the component values and the designators (Q1, Q2, etc.) so that it is easier to discuss the circuit.