We have had a fox problem over here from Day #1. We have a den close to our property and every year there is a litter of multiple kits. On any given day at any time of the year, we have at least 4-5 foxes around. Our neighbors also feed them, which is frustrating. We've lost a few chickens to foxes, but only when we free-range and if we aren't outside. We now only free-range if we are outside and only from May until October. It's annoying, but they were here first.
As far as whether or not the fox will give up, I guess it depends. The foxes around here have given up when our chickens are in the run/coop. They tried early on to get them and then realized they couldn't so they don't even try anymore. I lock my girls up every night at sunset and let them out at sunrise. Foxes do come around at night. We see them on the camera and their scat is everywhere, but they can't get my birds when they are inside their coop/run. Hope this helps some.
P.S. We do shoot at them with our pellet/bb guns if we can get a good shot off. It scares them away for a bit. Yelling helps too.