1. The disposition of a person which is unruly or stubborn: The intractability or obstinacy that little Timmy showed was very difficult to deal with, especially when it was time to go to bed!
2. The nature or feature of something that is hard to manage or deal with: The intractability of the leak of the faucet in the bathroom couldn't be fixed easily, so Tom had to call the plumber!
3. The inability of something which is not easily cured or relieved: The intractability of John's pain in his back was something that he had to put up with in addition to taking some medication which didn't help him much at all.