I tried to root an avocado pit in water with toothpicks as suggested, but gave up after leaving it for quite a long time. Finally I just stuck the pit in dirt and watered it. Six months later a tall skinny sprout came out of the dirt, and just when it was sprouting tiny little leaves my cat tipped it over and the top broke off. Will it continue to grow or is it doomed to die off and never grow again?
It depends if it has roots. When first sprouting the stored energy in the avocado feeds the growth of the leaves. If your plant has a few roots then it could sprout again.
If avocados are inexpensive in your area I suggest buying a fresh one and trying again. The avocados we sprouted with the toothpick method are now five feet tall and still going so that is a reliable method.