How are we able to break wire by repeated bending

We are able to break it because wire is elastic which means that it stretches. The more we stretch it the more the material comes off.

Repetitive bending cause metal fatigue which is responsible for the break of wire.

Explanation:

Metal fatigue is defined as the weakening of metal when cyclic load is applied on it. Due to metal fatigue cracks are grown in the structure and these cracks become the reason of metal breaking.

Moreover, If the repetitive bending is too fast, heat is produced. This heat changes the structure of atoms in the metal and make it more brittle. That's why metals break due to repetitive bending.