When my puffers had ich, it happened exactly the same way. They would get better for a few days, then it would re-appear worse than before.
I was treating the entire tank with a product called kick-ich by Ruby Reef. I got it at CCA. I'm not going to say it helped, but it certainly didn't hurt anything. Since your fish is in QT, your could safely double the dosage. I would slowly raise the temp to approx 85*. This causes the ich parasite to go into high speed life, and it will reach the end of it's life cycle faster. You cannot kill the parasite while it is on the fish, only when it is free swimming, so the faster you can get it to let go, the faster you can kill it.
Be sure, at high temps, that you run plenty of air bubbles thru the tank. Dissolved O2 will be minimal. Be manic about keeping the water quality high, and do lots of water changes, paying special attention to siphoning the bottom where the dead and dying parasites will be. Get them out of the tank on a very regular basis.
Try to get him to eat anything. Live guppies, live ghost shrimp, anything at all that will entice him to eat. Also, by the 7th day, your ich will be used to the hyposalinity method, so I would go ahead and slowly start to bring it back up.
If this is a fish you've recently gotten, ich is to be expected, but if this is a fish you've had for some time, you need to find out what caused the outbreak. Usually it's some kind of stress- adding a roomie, poor water quality, even strangers coming to visit.
In all honesty, I finally gave up on treating the tank, and figured if they got over it, they'll live and if not, they'll die. I did my best to keep the water quality high, and they eventually got over it, but they never gave up eating either.
Good luck!