TSU: The Honda transmission is incredibly reliable. It was/is built around the transmission used on the Honda Gold Wing for over 30 years. However, when water and grime are introduced into it, anything can happen. Most often, more (much more) than a flushing is needed.
Remember ATV (of any brand) means All TERRAIN Vehicle, and while the machines are sealed as well as possible, they are not intended to be boats.
I'd recommend a complete disassembly and rebuild of the tranny.