My first dog, Musquash taught herself to find them. I believe they do leave some scent when flying as she always knew what direction to go in. You might hear her going back and forth slowly as she searched, then she'd stop. Pretty soon you would hear her coming straight back out and you knew her tail was up, her head was high and the bird was in her mouth.pistol ehn yeah not a easy shot with that... it happens ...I had pointers and retriever and my experience is when they fly off then its pretty much game over for your dog, they can't follow the sent in the air... in your case if it initially fly off then fell and you chased it with you dog then yes you have a chance on finding it ... As dumb as these bird are they are master at diversion and camouflage sometime you think they flew off 300 ft in a straight line in the bush but then you find it 100ft in from where you saw it and off to the side while on your way back... or was it the same one ??
I mostly hunt with a 20 gauge because then if I see a duck I can shoot it, sometime I do hunt with my .17 but not often. I like hunting with my dog, they will inevitable make me miss a few opportunities but they will find a lot more bird that I wouldn't have seen without them... in my experience it take 3 season to have a pro hunting dog one can't expect too much of them the first two seasons. This year she started alternating between ground and air sent which is nice to see, she figured out they are not always on the ground.
She used to bring them back alive but must have gotten pecked as after a few years she developed a harder mouth.
One time I was with a coworker heading into the woods to start cruising. He stopped and shot at a bird but it flew off and he made no attempt to find it. We went 1/4 mile down the road to establish his starting point which just happened to be where he shot at the grouse so I opened the door and said " go find the bird." There was no hesitation, she ran down to where it had flown from, took off into the woods and came back with it in her mouth.
The last fall that I had her, birds were hard to find. I only shot one, that was in December with a foot and a half of snow on the ground. She was all crippled up but bolted out of the truck, ran to where it fell and started bringing it out. Several times she fell and I had to help her up but she wouldn't let go of that bird... I think she knew that it was her last one. I put it in the freezer without cleaning it. Two months later I buried it with her.
Ruger was a year old when I got him and always had a hard mouth, which I attributed to being hungry for the first year of his life. Yet he still liked to retrieve, I just had to be right there or he'd eat it. He could be sound asleep in the back seat but all I had to do was reach toward the gun and one eye would open... pick it up and he'd be looking around for the bird.