I keep my pop doors open 24/7, except when it gets below 40 degrees. The run is 1/2 inch hardware cloth on the bottom 3' (and buried 6" down and 6" out). The top half is 1 x 2" hardware cloth. The roof is chicken wire.
My coop is enlosed also but I never leave the poop door open at night,as soon as they are all in it gets closed.If something wanted to dig under the run at night it might take them an hour or so bt they would have access into the coop,and I only have chicken wire enclosing the coop and a strong aimal would be able to make a hole after some work at it.
There have been occasions where I've left my pop door open - a few nights when it was unGodly hot, or when I was gone for a weekend and disabled the autodoor in case power went out - didn't want my chicken sitter to have to worry about it. But 98% of the time, the pop door gets shut. I guess I'm just too paranoid about night-time critters (and that's with a motion sensor security light above the run and a nightlight inside the housing). They can run or try to fly away against daytime predators, but they are totally helpless against nighttime ones...
We leave our pop door open all the time. Our run is made out of chainlink fence and is very secure. That way in the morning the girls can come out in the run when they want to. We do close it when it gets too cold.
Our pop doors are open all the time as the coop is enclosed in a run that is covered completely (from apron to roof) with 1/2" hardware cloth. We didn't want to go any bigger on the holes due to minks, weasels, raccoon hands, etc. I have 11 hens that have been in there for 6 months, the people door to the run is always latched/locked. They are only let out to free-range under direct supervision.