Ask yourself whats in the egg aside from lecithin thats absent in your recipe that stabilize mayonnaise ?
If you realize that then you can solve that problem.
The rule in replacement of ingredients is pretty simple ; know what are the components of that material and whats its functionality in a particular application. Then from there source out viable alternatives that would fulfill that functionality…
If you did not think if it in that way…then you are not qualified to do the work you are assigned.
From the concept of mayonnaise preparation, the most important component is the egg- which you replace with soya bean oil.
I can just imagine your product separation- water separating from the oil. This means you lack the ingredient to replace the lecithin- which is inherently present in the egg. The lecithin enhances emulsion stability and improves product appearance and texture.
So, add an ingredient in order to emulsify the oil and water and other ingredients.