Opponent casts Runaway Carriage, then True-Faith sensor…oh know I thought, how will I survive…but then I cast Demolish to say Good Bye to that mean ole support card, and remove the Vigilance from the creature. No such luck. Despite being destroyed, the effects remained…I lost the match because all of my creatures crashed themselves against an unkillable foe.
I was using Koth, the opponent was Jace. There were no other opponent supports on the board for the remainder of the match.
I can confirm this as well. The additional bonus for the target being human also remains, and also stacks if a second one is cadt after the first is totally destroyed.