Infinity. Why? Because by the time an Unbreaking Infinity bow is broken, you'll have enough experience to make another one. Depending on how many arrows you use, though, you may at some point run out of arrows.
If you are planning to make a suggestion, please read this.
If you want to know more, you can read this.
For those who complain about post-Beta generation, you might want to see this.
Quote from Zeno410»
Banging your mouse a lot is not a skill.