How do you gain the confidence of an extremely wary dog?

You are doing the right things. The key is not to push or force it to happen. Sometimes it helps if there's another dog around. It may bring out the wary dog by making him/her feel more comfortable. I sat with a dog that was very nervous because she wasn't used to being around anyone but her owner. I did not reach my hand out to pet her because that made her nervous. What I did is talk calmly throughout the day so she could hear my voice. When I put her food down, I made sure to step away to another room where we could still see each other, but she felt free to eat without me hovering. I also let her have her space. Another thing I did was sit on the floor a lot. That can sometimes be less intimidating when a dog sees you more on their level. After the first day or so, she started to sit next to me on the ground and let me know when she was ready to be pet. I didn't go crazy with the affection either until she was more comfortable. Also, some shy dogs take more to either the male or the female in the household. Observe, and they'll let you know.

Keep doing what you're doing and let him do his thing. Don't attempt to approach him unless you absolutely have to. The more you push it, the more likely he is to continue to withdraw. He'll be far more likely to come to you when you've proven to him that you're not going to push him beyond his limits.

Keep tossing him good treats periodically when you're in the room with him and he'll start to associate you as the source of good things. You can also try to play a little game with him, tossing him treats whenever he does something "brave" (like leaving his corner at all), or putting a really yummy treat somewhere in his sight lines while he's watching so that he's enticed to play hide and seek. gradually increasing the distance he has to go for the treats and eventually placing them under or behind things so he has to hunt more and more. You can also give him puzzle toys/stuffed Kongs to keep him occupied and help him stay relaxed.

Just give it time and he'll at least get comfortable with your presence, even if he never wants touch or affection. Some dogs are really slow to trust, but prove to them that you'll keep him safe and secure and you'll go far with him.

I've experienced this where some dogs just never click with me during a stay. I would just let them have their space, but also know you're still there. Maybe try to toss him a treat each time you walk by, or just say hi, in an upbeat tone so they know you're not going to hurt them.

I absolutely agree with the ladies above -- give him his space. I had a dog that was a little hesitant with me, and one night he jumped on my stomach and licked me uncontrollably --- we have been great buds since then. I think time and space are key here -- when he sees that you mean him no harm, he will (hopefully) come to trust you and open up to you. Good luck!

I too agree with the above answers. I will give a wary dog space and go about my business. I will keep calm around the dog and eventually I will try to give the dog a treat or set one close by and walk away. They generally warm up pretty quickly when they realize I am their person for the time being. I have had a couple dogs in the years past that were unfortunately mentally unstable, near the end of their lives and actually violent. In those situations I did the best I could to take care of their basic needs and protect myself. It also helps to be a goofy dog yourself. I often will mimic happy dog body language, that usually perks up a wary dog:)