They made a serious mistake at some point if they had such a large advantage and allowed you a perpetual check. The game would inevitably have drawn by three move repetition after some time, so you certainly should not resign as you were not losing. You could offer a draw if you prefer not to win on time, but it's not your responsibility to resign after your opponent blunders.
Edit: If the engine still showed a -10 advantage for your opponent, you could not have indefinitely checked their king
Playing a 10 min game, and I was kicking some butt. Analysis afterwards said I was Up +26 at one point. And then 1 move brought me back to 0.00. Whoops. Somehow, I managed another blunder afterwards. Double whoops, Thought game was over (comp had me at -10 at that point). But I noticed that my opponent only had 30s to my 2 mins and that I could indefinitely check his King. Should I run out the clock or retire?