How long can I keep raw-egg based salad dressing refrigerated
Without testing samples regularly to track the rate of growth of harmful bacteria, this is a hard question to answer, doubly so without proportions of ingredients.  Salt and vinegar will slow bacterial growth, but will not stop it unless you add unpalatable amounts.  Garlic has some antimicrobial activity, but it has not been well quantified, and does not operate against all bacteria.  Refrigeration also slows growth, but each fridge is different, and how the family uses the fridge (staring at the contents while deciding, for instance) can alter the true effectiveness.

Personally, I would treat the salad dressing the same way as plain raw egg yolk -- four days if kept well chilled.  The salt and vinegar probably buy another day or two, but I would not count on it.