It shouldn't matter when they bill you/insurance company, only the date of service should matter. So you shouldn't have to pay your deductible again. Of course, if you have PT or follow up appointments, you will have to continue to pay since they will have a different service date.
Also beware of bills that the hospital may send you saying that certain things weren't paid by the insurance and now you are responsible for them. You may not be responsible for them.