It is said that the fasting "regresses" through past issues. If your problem is near the top of the list, in other words fairly recent, then you may be able to do it. If not, you will need to extend your fast or do some follow-on fasts.
Is there a test they can do near the end of your fast to see if you've licked it? If the test shows you still have it you can continue to fast until the test shows it's gone.