All the blender does is emulsify the mixture--it has no effect on how long it will keep before the dressing begins to spoil or go off.
Normally, oil and water do not like to mix. The oil will coalesce into droplets, then rise to the top due to buoyancy, so that you will have a layer of oil above the water-based liquids. Blending the mixture will break up the oil droplets into very small droplets. These take much longer to coalesce together, so you have a creamy dressing for a time.
Over time, the oil can coalesce and separate back out. If this happens, assuming the ingredients have not spoiled, you can always remix or re-blend the mixture--it s not a safety issue.
I suggest storing your dressing in the refrigerator, where it will be good for several days, probably up to a week, although the oil may separate out.
You can freeze it, but this is likely to encourage the emulsion to break.
Note: I have not discussed emulsifiers like lecithin from egg yolks or mustard which help keep oil-water emulsions stable, because I don't see any in this recipe.