I've drained the fat from a roasted duck, placed it in a closed container, saved it in the 'fridge, not quite sure how long it will last??
The main concern is keeping it from going rancid which is due to oxidation and heat. If you keep it at the back of the fridge in a container that minimizes the amount of open space on top it will keep a long time.
You can also freeze it if you don't intend to use in the near future and don't want it taking up space in the refrigerator.
Should last ages as the other posters have said. However make sure it's pure and doesn't have anything else from the duck in as that can go off earlier meaning you have to throw out the fat with it.
At least 6 months, easily a year. You'll use it all up well before then or you don't deserve to own duck fat.