I would definitely check other areas
I’m leaning more to him flying away because there was zero sign of blood or feathers. That would rule out most predators
Only ones I can think would be hawks , owl ect that could fly in snag and take off
Although often they do fight the catch right there...
You can add coyote rollers to the top of fence to stop them but a regular fence they can jump
But you would most likely seek signs of feathers somewhere
A hawk could snag a bird and take off very fast
But I’m going to pray he just flew off and hopefully shows back up