What is the effect of oxygen on soap foam?
Hmmm. I don't know, but I'd say that if you significantly lowered the percentage of $\rm O_2$ in the air, the average molecular weight of the molecules in the bubble would drop (there'd be more low-molecular weight nitrogen and less higher-molecular weight oxygen), so the rate at which gas would diffuse out of the bubble would increase, and the foam would flatten faster. 

Try blowing a foam with nitrogen, and compare it with the results of blowing a foam with air or oxygen---if I'm right, the foam blown with nitrogen will flatten a bit faster.

There'll be a bit more $\rm CO_2$ in the air from the candle, and that would diffuse more slowly out of the bubble (in fact, $\rm CO_2$ is used as a "blowing agent" to make foams, partially for that reason). But I'd think in this case that the small amount of $\rm CO_2$ produced by the candle would dissolve in the liquid, with gas dissolution rates enhanced by the lower surface tension and higher surface area of the foam.