I find that my mayo doesn't thicken until sufficient oil has been added, BUT I also find that if I go beyond some critical point with the oil, it will thin again and be spoiled. The answer to fixing thin mayo may be counter-intuitive.
When I read up on why, I found that there are two kinds of emulsions, one in which oil is dispersed in water and the other in which water is dispersed in oil. While the large amount of oil versus the small amount of water in mayo might make us think otherwise, it's an oil dispersed in water type emulsion. But that makes sense. We add the oil to the water (in the vinegar, lemon juice, etc.).
In making the emulsion, oil particles must be dispersed, made very fine. The more of those dispersed particles, the thicker the emulsion. But if you add too much, it becomes impossible for them to avoid each other, and they begin to clump, and the emulsion "breaks."
Emulsions are unstable by nature. They want to separate. In mayo, egg is our stabilizer. A stabilizer provides a large molecule needed to keep the fat particles apart.
It usual instruction is to begin by adding oil very slowly and increasing the doses as you go along. That's mostly important with low power dispersion, such as with a hand whisk. With an immersion blender, it's hard for the fat to escape the high energy milling produced by the blender, and you can go significantly faster without the oil pooling on top.
So, if you use far too little oil, there's not enough emulsification, and it's thin. If you use too much oil, the particles combine again and it gets thin. If it once was thick but begins to thin as you add oil, stop the oil, and add more vinegar or lemon juice to give the dispersed fat particles room as you blend it more.
"Kitchen duty is awarded only to those of manifest excellence..." - The Master, Dogen