I'm so happy that things are looking up for you. If things do fall back again, here are my tips:
Personally I wouldn't rule out pain. Based on what you said in the past posts, if he does this only over time like 20 min into the ride OR if he is ridden more than once a week, my first thought is some kind of pain. I completely disagree that he is spoiled because he backs up. If the issue persists, try lunging him on a line WITH!!! A rider. If he lunges like a dream on the line, he should listen to that on the ground while also having someone on him asking for the same commands. If he continues to act like that, I would highly recommend a vet. If he doesn't then you know it could be more of a training issue. If he reacts to the crop so violently, try having your trainer or a friend on the ground use a lunge whip at/on him to drive him forward. Let him throw out his little fits.
I'm not sure which horse trainer it was that said this quote (I don't really follow them, nor any method, as I believe each horse is different and needs to be handled in stride, so I take each issue as they come) but the best advice I've EVER been given/heard is: "Make the right thing comfortable and the wrong thing uncomfortable". I think it was some famous trainer who said that. Anyway, that is more of an ideal then a method, I think, and I've found it pretty much always works. Keep it in mind with any future issues. Someone suggesed -telling- him to back when he backs and that may or may not work. I would try spinning him in circles one way or another. You want him to learn that his choices, in this case backing, are going to be really hard and alot of work to handle, where as your choices, moving forward, circling, etc, are the "fun" choices as you make them easier and less work. If he doesn't want to circle, make him. Do a one rein "stop" and pull his head, much like you'd do if he was bucking, and kick, kick, kick until he spins. Doesn't have to be fast. Just circle circle circle circle until he is sick of it, then stand still. If he won't stand, circle circle circle! His ideas are the hard choices! It will be more comfortable for him to walk forward than it will to back up and fight the entire time.
I also agree with the 'bored' thing. My mare comes up with "interesting " things to make my rides more, well, interesting, when she gets bored. A change of enviorment or a change of lesson seems to do good. Keep his mind -always- focused. He won't have time for anything but listening to you!!
And good job working with him!! Have fun too, when he isn't driving you nuts, haha!
~He knows when you're happy
~He knows when you're comfortable
~And he always knows when you have carrots.