Maple does have sap (think maple syrup) I wouldn't think a lot would be in a small branch that was heat treated, but it might have done something.

Could it be the rubbed places on his side became infected? But you'd probably see redness and swelling there.

According to some sources I've read White's live in a variety of places and should be tolerant of 50% humidity though that may be a little low. People can't seem to agree on the proper humidity, but I doubt the humidity would directly harm the frog much by itself. Unless it wasn't soaking which you said it wasn't. Hm.

Seconding the thing about distilled water, but you knew that.