All advice you've been given is spot on and needs to be followed without question. If his mouth is open and he can't close it then why are you not supporting his head to keep it out of the water?

You must ALWAYS treat the water used for your frogs especially if its well water or tap water. Assuming that it is fine is foolish. The chemicals and heavy metals are very detrimental to their health and will poison them. Lack of a calcium supplement within the frogs diet is the culprit here. I would also go out and buy some Fluker's Repta-Aid(Repta-Boost) and use it orally and place a two scoops in his bath. Buy some UNFLAVORED PEDIALYTE and prepare a bath at a 10 to 1 ratio. So for every 10 ounces of Luke warm DE-CHLORINATED WATER add one ounce of UNFLAVORED PEDIALYTE. add two scoops of the Repta-Aid(Repta-Boost) to the bath and while you support him be sure to pour a little over his back as well. Soak fir 20 minutes After that bath have a second bath prepared of only Luke warm DE-CHLORINATED WATER to rinse the Repta-Aid(Repta-Boost) off his skin. so no bacteria or fungus tries to grow on his skin. Repeat this bath every other day and keep us updated on his progress.