Well, it usally depends on who mods your stories. Your stories may be validated often, but different mods may be approving them, so they don't necessarily see your consistency. I can't really give you an exact time frame, though. Sorry.
EDIT: DA RULES FOR REQUESTING AUTHOR VALIDATION] (copypasta'd and edited a little from DG)
-You must have at least five (5) posted stories and/or chapters and a total, combined word count of at least 5,000 words written. If any of your submissions have been denied in the past two (2) months, or if it hasn’t yet been two (2) months since you last requested validation, you can’t ask again.
-Author validations will be stricter than story validations – it’s the difference between a lifelong pass and a one-time thing.
-Request in this thread on the forums, in the announcement comments, or e-mail one of us. Make sure you include your username, and that you check PMs (on the forums) and/or that you have a working e-mail address associated with your account so that we can get back to you.
-Two (2) of the mods will decide whether or not you will be validated. If they are in agreement, then that decision will stand (you will be validated or your validation request will be rejected). If not, then a third mod will come in as tiebreaker.
-You will be contacted privately with the decision, including suggestions for improvement. If you aren’t validated, you can ask again, two months after your author validation has been denied.