Wobbling feral cat problem

Question
Our family has had 2 cats for years as the kids grew. Several have passed in their time, and so we have none now. But the oldest (age 19) daughter has begun "adopting" stray cats to fill the emotional void in our lives. Of three that we feed on the back step regularly, one worries us. After five or more years of seeing this orange feral cat arrive cautiously to feed alone, we have seen a shocking change.
After a 2 week vacation, we return to find that cat is wobbling badly as he moves. His movements are exagerated and look like over-correcting. His sleek, hunter style stealth is gone. His coat looks wet, he sits in the rain, not moving under shelter, and eats less dry cat food we set out for him. High heat & humidity in the S.E. Ohio region have spawned a lot of flies that return to the uneaten dry food. Fresh water set out every day is used by all animals, racoons, cats, birds, etc.  We have a live trap, used to take racoons away to the Dog Warden's disposal. But we have never caught a cat in it. We might trap this orange male cat, but it would destroy any trust we have been building. He now would run up to feed before we got the door closed, prior to our trip. We have NEVER touched him. He is too gun shy and always keeps his distance, but seems to trust that we will provide food and a feral cat shelter for him to sleep in. We see him each morning and at twilight for two feedings a day. There are two other cats who are tame and eat from the same bowls at other times. They tolerate each other, and will come inside if we let them. They are tame. He is feral.
Please doctor, advise us what to do for our feral friend. We worry for him and are shocked by this unsteady, wobbling behavior. (He had a cream companion some years ago who appeared dumber, deaf, and has disappeared last year...possibly died, as he seemed to be in frequent fights due to his slow nature.)
1) Do you think Orangy is treatable?   2) Should we attempt to trap him, and with what bait?  3) Any advice on how to get him and not the other cats?  4) Do you think this condition is terminal and how long does it take?  5) IF we can trap him, do you recommend he be "put down?"  Please advise us.

Answer
So this is a continuation of the question asked by another family member.
1. I think it may be very difficult to treat Orangy, since the treatment may be too stressful for him since he has never  been held. Sometimes the best thing we can do for an animal is to let them follow their journey on their own, to their own end.
2 & 3. I would attempt to trap him. I am not an expert in this area, so contact your local feral cat association. There is an excellent one in my area, Prince Georges Feral Friends who does a lot of education. they also teach a lot of holistic approaches, so your daughter could learn a lot from them. www.PGFerals.org
4. As said in the prior answer, there are way too many conditions that can cause these symptoms to have any idea how he will respond. One that I did not mention is Rabies. It does cause sudden illness, especially with neurological symptoms just before death (within 10 days of death, so if he has been ill more than 10 days it is unlikely to be Rabies), so do not get bit by him. If he does die, look hard for his body and have the head tested.
5. Deciding to help him die would be for your veterinarian to help you decide.
I hope this helps in addition to the earlier answer.