What is the frequency of the "Quality Filter" for re-evaluation of the account which has "Ask Question" Ban?
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From what I've heard from the SE team, there is no "Quality ban" that actually exists on your profile, only a check that is run on your account at time of posting that returns the "Sorry, we are no longer taking questions from this account" message. At any given time you will either be able to post or get the failure message; that's about as substantial as the "ban" really is.
So the "check" is really when you try to post. If you have actually improved your posts enough to no longer be banned you should theoretically be able to immediately post questions again (barring caching).