Posted: Mon Dec 08, 2014 12:30 am Re: Weakening Turtle!
Some pictures of your setup would help in this situation, as well as a quick summary on how your other turtle is doing.
The way I'm interpreting your post, it sounds like while you have provided the turtles with an area to dry off, you haven't addressed their need for proper basking conditions once they get to the dry area. This can be a problem, since basking areas that aren't warm enough often cause turtles to stay in the water. What concerns me is that this isn't the case with your weakening turtle. I would consider its behavior an attempt at "excessive" basking, considering that you mentioned it's been staying there for a while--even though it sounds like it didn't have any heat to entice it to stay up there. If it's swimming funny, then the basking could be a symptom of RI. This would also be supported by the presence of what sounds like gaping (the gasping) and accompanying mucous (the white stuff). Oddly enough, though, RI usually only comes around when both basking and water temperatures are too cold, but your water sounds warm enough.
Finally, a side note about the diet--your RES is just a baby, so you don't need to push too many vegetables yet (unless it eats them willingly already, in which case, please keep up the good work!)
Again, any pictures you can get would be a huge help in identifying the problem. If it does turn out to have RI or something similar, please separate the turtles as soon as possible and get the sick one to a qualified reptile vet. This is especially urgent, considering the turtle's size/age.