Neons only show good strong colours when they are happy in their enviornment and are fully healthy. They also go pale at night when the tank lights are off, to me this indicates that the fish use their colouring to signal mood and health.
If one is lying on the bottom and gasping, it is a grave sign, I have rarely seen a full recovery from a state like this, of course its no reason to give up hope.
There are unfortunately many things which could be wrong here so we need to look at the wider picture.
Are the rest of the neons acting strangely? Neons will shun a sick member of the group so if he is left on his own a lot, the neons have spotted an illness quicker than you or I could. If conditions in the tank arent right for them, neons will also become aggressive to each other and often swim with the head in a downward position.
What are your water parameters? Neons have not evolved to handle water pollution such as ammonia and nitrite at all because their natural habitat has a PH below 7 which makes ammonia much less toxic. Therefore a lower PH is better suited to these fish but is by no means an absolute necessity as far as neons go.
Same goes for high nitrates and low oxygen, if you have one, add an airstone to break the water surface and add vital oxygen, especially at night.
How will you medicate? Personally, I would avoid medicating a tank if just one neon is sick, they arent the sturdiest of fish and some will naturally succumb to parasites that others can handle easily. I find upping the temp to 84F for a few days a good tonic for the fish and should bring any parasite or bacterial problems to a head so you can tackle them rather than letting them creep up over a longer period. It also boosts metabolism and can sometimes get a moping fish eating and active again.
Keep us posted on how you get on, and dont be too hard on yourself if you lose him, sometimes it just cant be avoided.
Ken