I always use a blender to make the mayonnaise base for blue cheese dressing. The blender struggles a bit as the mayo gets thick and the blender doesn't want to move the top of it, so I have to stop and scrape.
I used the food processor the last time I tried mayonnaise and it worked, but I had to put everything but the oil in before the blades could move the ingredients. One egg yolk took up so little space that the blades went right over the top of it.
You'll have better luck if you whip the eggs for a bit to develop the lecithin before you start dribbling oil. Once the eggs have been whipped for a bit, they will emulsify with the oil better.
I'm making blue cheese dressing today and I think I will try using the food processor and see how it works. I'm a little nervous about changing anything from what works. It appears that some people can make mayonnaise easily and some people can't make it to save their lives. I'm in the camp of people that mayonnaise doesn't want to emulsify for, no matter how carefully I follow the directions. It's doubly frustrating because the blue cheese dressing always turns out perfect and I'm hopeless with mayonnaise, even though it is the same process.