So there is evidence that some fish may be able to 'fight' ich and maintain a subclinical infection. I've never seen any data showing that they can clear it. There is also some evidence that strains of ich may eventually die out. Taking these two together, it would appear that if you keep your fish healthy long enough and no new strains of ich are introduced, it may eventually die off and the fish would be 'cured.' This plan has far to many 'ifs' to be considered a plan, IMHO, and you are experiencing one of them.
Ich manifestations are cyclical and can be harbored asymptomatically, which makes verifying a cure difficult and also is likely the source of many claims of 'cure.'
At this point, you can either decide to live with ich and hope it doesn't get bad enough to kill your fish, or start treatment and keep your your DT fallow to clear it. Since this is a puffer, I'm assuming it is not a reef tank. If this is the case you could potentially treat your whole DT, since you don't have corals to worry about.