I am curious about which creatures in the hospital you have more/less sucess with.
I would guess that hedgehogs do quite well as they seem to be fairly relaxed about human contact and tend to be easy to spot and catch if they are unwell. The other end of the spectrum must be deer who seem to drop dead if you as much as look at them.
A surprise to me was that small rabbits don't do too well - I expected them to be pretty sturdy.
Hedgehogs are the most common mammal that we treat at the hospital & yes, they are fairly easy to deal with & the survival rate is pretty good provided we get them in soon enough. People do have a tendency to hang on to wildlife, especially hedgehogs, for a few days before bringing them in, by which time infections have got a good hold & are much harder to treat.
We have struggled with baby rabbits in the past, nothing to do with stress, but I think we have now mastered the art of rearing them (fingers crossed) & we have had a good success rate this year.
As you say, deer are difficult, very highly strung creatures which is why we tend to sedate deer to bring them in to the hospital.
Other species prone to stress & difficult to deal with are: sparrowhawks, kingfishers, woodpeckers, moorhens, coots & hares.
Yes, I'm surprised at the moorhens and coots too - one tends to think of them as fairly bolshei sort of creatures. The others you mention I'm not too surprised about, though!