Moving him around is not a good idea, unless his tank is really in bad shape. Moving already sick and stressed frogs to unfamiliar surrounds can often provide the final amount of stress that they just can't handle. When I have a situation like this, I reduce the amount of stress a frog receives as much as I can.
First, keep his tank humidity very high. This will keep him hydrated and more comfortable in his surroundings. A butter tub with 2/3 of its wall height removed and filled with water or very diluted pedialite also helps. Keeping him hydrated is extremely important. Second, don't keep dumping food into his tank. Having bugs crawling all over a sick frog is another big stress factor. If you can find damp-wood termites, throw a couple of these guys in at a time and see if they get eaten. I usually don't worry about dusting in the beginning, since putting on weight is often the #1 concern. If you can't find termites, use whatever you have. If your crix are pinheads, then they are fine. If they are any larger, feed them to your leos or let them go. Any common fruit fly will also do, although lethargic frogs are not going to chase them up the walls. So, dump a few flies in a tupperware container, put a top on it, and throw it in the freezer for a few minutes to slow the little buggers down. Thirdly, and this may be overkill, I tape black construction paper to the 3 exposed sides of the sick frog's viv. If you walk by a healthy auratus, standing in an open spot of its tank, most of the time they hide or at least move a little. Lethargic frogs don't want to move, but are still freaked out by the 5 or 6 foot tall monster standing less than 12 inches from them. So, blacking out their tank makes sense in my book.
Good luck with the little guy. I hope it works out, but if it doesn't, know that we have all been there.
~Joe