Well as long as you don't turn the diificulty to peaceful the wither will not dissapear, but it may wonder around the area. if you leave the area (the chunks unload) he will stay in place until you load the chunks again (get in the area)
Passive mobs (cows sheep pigs and stuff) are hostile to the wither so he will chase them and try to kill them, so he may move if there are passive mobs in the area.
Hope it helped