You'll do it! Remember to take measurements as well so that when the scales are being cruel, you can still see progress. Get jeans in the next size down out where you can see them, and try them on regularly, at least once a week. Mark belts so you can see the inches coming off that way, take regular progress photos etc.
There are lots of non scale ways you can see your efforts paying off. Look for those thumbs up moments and savour them, they'll help get you through the tough times.
I had a pair of size 14 skinny jeans fall down the other day. There is no food in the world that would make me feel as good as realising that the 12s are approaching!
The thing that derails you is letting yourself believe you won't do it, can't do it, don't deserve it. You will, you can and you do. Do whatever it takes to convince yourself of that, because on a diet this straightforward, nothing can stop you reaching your goal.
You've carried on when you struggled, you've carried on when the scales let you down and you felt despondent. If you can get through that, you can get through anything. Remember to give yourself the credit you deserve for the victories you've already had. They build a picture of who you believe you are. If you disregard your successes and focus on your failures, you'll convince yourself that you're a failure. If you acknowledge your successes, you'll start to understand how powerful you really are.