Mange is hard on coyotes but it won't take out all coyotes in an area. In good habitat you will always get fill in. Some areas worse than others, next to the indian reservation I have 60-80% mange problems other areas 20% mange problems. It can be in cycles that last 10 years or so. Coyotes are great at surviving and mangy coyotes will hole up in bale stacks, machine shed and other outbuildings when it gets cold.
Coyotes with severe mange I have noticed don't travel near as much and you can tell by there long toe nails, they don't travel to keep them worn down. They also will hole up close to carrion and try and live off every dead critter they find. They will be the first to come to a call or work a trap set. Even though they may have had a few bad experiances, the need to survive ussaly outweighs cunningness with mangy coyotes.
Here is a beauty from the other day! 