to be so tired, worried, or annoyed by something that you feel unable to deal with it any more
Usage notes: An animal which is tied up by a rope cannot reach the grass which is further away than the end of the rope and becomes hungry and unhappy.
After a day with four screaming kids I'm at the end of my tether. He's out of work, hanging around the house all day and at the end of his rope. (
British, American & Australian)