It is possible to change the next payment date, but it will simply move the next payment date forward, not update the whole series. For example, if the donation charges monthly on the 1st, and the September payment was missed, you may change the next payment date to be September 15th. This would move the October 1st payment forward. No payment would then be made in October, and the next payment date would be November 1st.

To capture September and October, cancel the old gift and create a new sustaining gift.