He may not want to do so to prevent Andrew doing more harm. By Andrew not using his styles the result is the same but it's less harsh as it is voluntary. The king has enough problems dealing with the desire of his youngest son and his wife to make money out of their relationship to HM.
Besides if he takes Andrew's he might be forced to take Harry's as well.
Another reason might be that once you strip one Prince of his style and titles that may come back to haunt you or your successors when they could do without the bother.
Andrew may be an unpleasant man but so far he has not been convicted in a court of law. Remember how unpopular the King himself was while his first marriage fell apart and after the divorce?