Vitamin E may help protect against rancidity (it's an antioxidant), it provides NO protection agains mold and bacteria which you do need to be concerned with in a scrub.
So to answer your question of how long, I'd say no time.
If you are making single use-sized scrubs with no water in the mix I don't think it's an issue because it's the water that is problematic. But once water is introduced by wet fingers, steam, splashing and splattering in the shower you have really no time at all.
I just made body scrub with it...
