My chickens and ducks (housed together) have access to their run 24/7. The run has hardware wire on the top, sides and fully lining the bottom. The wire is screwed in with hex-head screws and large flat washers. I have at least two swivel hasp latches on all doors and the hinged top, with carabiners through the swivels. Even the run is screwed to the coop rather than nailed.
Where I live in the foothills we have bobcats, mountain lions, skunks, possums, raccoons, etc. I like the fact that my birds can be outside when they want to and don't have to wait for me to let them out. Also, if I happen to be late returning home I don't need to worry about rushing home to lock them up.
Personally, I don't rely on chicken wire to much more than keep chickens in. I didn't even use it to line the bottom of our run, which is buried under about 6" of dirt.