In an ideal world, we'd aim for about zero seconds between impact and death. The means using the right tool for the job to help ensure that. It's not always going to happen though.
I have shot plenty of critters with air rifles. But after shooting possums with 22's and seeing bullets either ricochet off their heads or come to a dead stop against their skulls, I'm not sure I would want to tackle one with an air rifle. They can be tough little buggers. Dropping from a tree isn't going to put the final nail in the coffin either - they aren't that heavy and bounce quite well rather than going splat. I usually go for neck or chest shots on them with the 22 to make sure there's a soft meaty bit there to for the bullet to dump its energy into. That can result in them clinging on for a few seconds. No drama.
We have no way of knowing if you walked past your one a dozen or more times in your search any more than you do. But if it really was not there then it must have crawled (and died a somewhat slow death).
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