I get requests in rescue all.the.dadgum.time for service dogs. Most of the time we can't help. Most of the people asking have no clue what they need.
They often want the shy dogs, thinking they can "train them" to do service work -- uh, no.
The problem is there's no universal understanding of what people want in a service dog. The dogs who can help with daily living tasks are very, very special -- and need a special temperament and problem-solving ability. The ones who are PTSD support dogs don't need to do complex tasks, but need to be calm and highly attuned to their person.
Our rescue has had modest success with a few PTSD support dogs for veterans. It's training that good dogs can succeed at, without a high washout rate in the programs I know of. If I have an app from a veteran, I look for young, healthy dogs that have "bomb-proof" temperaments -- easy going, no environmental issues, no dog reactivity, low prey drive, very comfortable with people of all ages. These are dogs who can go anywhere around town.
Those dogs tend to make really good PTSD support dogs -- but I only see a few of those a year. I often tell veterans we work with the process can take months until we spot "the one."
In rescue, there's no shortage of placements for that kind of dog though (as they also make great family dogs for people with young kids!). We thus have to believe the vet is going to be a great owner, and the dog will have an excellent, happy life. More specialized service placements make me nervous because of the wash-out risk: even well bred pups have a high washout rate in complex service tasks. I'm not placing dogs in homes where there's a high washout potential, and washing out means that they will lose their home.
Interestingly, I know of one PTSD support placement that worked out well for a great dog that checked all the boxes -- except it had separation anxiety. It was extremely hard to place because of the severity of its SA, even though it was a bomb-proof, perfect dog when its people were around. The solution of being a PTSD support dog ended up being a win-win for the dog and the veteran, who takes the dog to work, to the store, and pretty much everywhere. It's was kind of a think-outside-the-box solution for a great dog who was having trouble getting placed, and it worked out astonishingly well. It wouldn't work for most dogs with SA because they've usually got other fear issues -- this one just happened to have been a great workingline dog who was otherwise quite sound.
I do know of a rescue dog who became a seizure alert dog on her own. She was an unusual dog had the best nose of any dog I've ever seen--relentless in tracking down hidden toys, leashes, etc, and using the breeze outside to find them even after we put them up far away, out of site to get her to settle down. She was adopted by a family as a pet, and she attached to their child. When the child started having seizures, she started alerting to them, all on her own. My theory is that she could smell the metabolic change.
I've had other families with sick kids ask us to find them a dog like that, and I just don't think I can do it -- she was a gift from Upstairs for the people who adopted her and put in the time to train her and develop a deep bond with her. Ironically, she was a dog who scared the living daylights out of shelter staff when she was there. She was a huge, sable, imposing girl -- and bossy with people who could be pushed around. She would drag the staff all over the shelter, and even sometimes would bite up the leash, stopping just short of a hand when they tried to move her around the facility, trying to get them to drop the leash so that she could take off running. She was a love when we met her though because we told her "no" and took control of the leash without fear, which caused her to relax and show us she was a terrific dog in her temp test. She just needed to know her humans weren't pushovers. Luckily, the family who adopted her was GSD-experienced and gave her good leadership from day one, which opened up the potential she had....and they were well rewarded. It's not something I know how to replicate though.