I had a lot of trouble when looking as well. I spent a good long while searching and sending out applications after applications. None of the rescues turned us down, but either they didn't get back to me, or they just never had a dog available that fit what we were looking for and when they did.... they blew us off on times to meet them. I sent out a lot of emails during this time, and called often. So if they missed THAT many attempts at contacting them.... they really really need to reorganize. I had a good home lined up, experience, and a trainer in place. You would think they would be thrilled. Out of 10 rescues contacted (this doesn't include individual rehomes, shelters, and petfinder ads) only 2 got back to me. One matched us to an awesome dog that I thought would fit... and then decided at the end she wanted to keep her instead, and the other just never fully went through with meet and greets.
It was extremely stressful and I ended up throwing in the towel. Just when I gave up all hope, a member on here mentioned about Duke being available for re-homing through his breeder. We fell in love with him and took him home.
The next GSD (Storm)... we purchased from a breeder. Which this was also done because I wanted to be more involved in the sports and needed a GSD bred for it. However, I'll be 100% honest, other then the humane society, or shelters.... I probably wont go through a rescue again. No offense to anyone here, but what a freaking headache. I'd understand if I was questionable.... like... lived in a studio apartment, no fence, no vet or trainer lined up, no experience, low income... etc. None of that is true, and I had NO problem giving them the $250-400 they were asking as an adoption fee. My dogs are spoiled rotten here.
Back when I used to volunteer and foster for rescues... I just don't remember it being so difficult for good homes to adopt. I understand the rescues have a lot on their plates, and can understand their side of it (I've been on that side too).... but, there are some rescues still out there that really need to learn to be organized and loosen up a bit. Many excellent homes are being passed by..... one dog out to those homes, is room for another to come in!
Anyway, I'd love to be confident in saying keep trying and don't give up.... but, at the same time I completely understand your frustration and didn't continue myself... so it would be silly for me to say something I can't stand behind. Maybe it's time to try stalking your local humane society.... they may not be as well evaluated, and may need some TLC, but I am sure some make their way in and it doesn't take too much to adopt from them. Lots of great dogs have come from those places.
Good luck on finding your next one.... whether they are rescued or purchased, I'm sure they'll have a wonderful home!