It last quite a bit, because the sugar cooks the milk. If you leave it inside a glass jar inside your fridge it will last.
Plus I don't think its going to last that long if it comes more or less okay, because you will put it on everything.
My favorite variation comes with infusing the milk with a flavor, like for example Earl Grey Tea and you get an Earl Grey Dulce de Leche. You can also add cinnamon to the mix while boiling to get another flavor.