Combustion is the oxidation (usually fairly rapid) of (usually) hydrocarbons. The rate and energy release depends on the amount of combustible material and oxygen available. An oil "candle" burns the vaporized oil drawn up a wick from a reservoir. Maintaining a flame of any sort requires a minimum heat generation from the combustion (fire triangle).
So, the question is just how slowly can you combust olive oil to maintain sufficient heat to continue the combustion? As most candles are not used for heating purposes, I must assume empirically that the burn time of 2-3 hours per ounce of olive oil (I didn't test that claim) is pretty close to the minimum sustainable rate. Extending that time by three times means that the rate of combustion would need to be at least three times less. That is unlikely to be self-sustaining.
It might be possible to use a very tiny wick (a piece of thread) for a much smaller flame. That would be an easier empirical experiment than trying to calculate the heat and mass balances for a flame (although that could be a good problem for a student).
Best regards,
Steven
