From what I have read, waste oil needs a continuous spark. Because of impurities in the oil (water, antifreeze, etc...) there may not always be a continuous fire and could cause the fire to go out.
I have had ignitors go out, but usually they quit all together. Some primarys are meant to be intermittent, so the ignitor doesnt have to run continuously, but if your furnace never did this in the past, I would doubt you have one of those.
Could the electrodes be shorting out somewhere?