I am nearly always in favor of letting native predators be. I have lost many fowl to them over time, but I still let them be. They are essential to a healthy ecology, and they are hard pressed enough with overdevelopment, loss of habitat, and over-hunting, without being killed for the act of taking their dinner where they can find it.
That having been said, I would make an exception in this case. An unhealthy fox running around near people in daytime is a danger to itself, to the healthy population of foxes, and to the people and pets in your area. While it probably would prefer to live, its existence and persistence in populated areas (in daylight), brings attention to itself and to any other foxes that might be out there, which is usually bad news for predator populations. Furthermore, if it is ill, it is running around spreading illness to every fox and potentially every canine it comes in contact with.
If you're not able to do the deed yourself, you can call in animal control OR you can probably find someone (try craigslist) in the area who would appreciate the opportunity to hunt the fox for sport. Many hunters are extremely responsible and respectful, and a good hunter should be able to put the fox out quickly and relatively humanely. Just select your hunter carefully--and make it clear that you are authorizing him to kill this particular fox ONLY.
Good luck!