Most wines go *bad* after opening because they become oxidized. Marsala is a wine that is *already* oxidized, and it's that oxidation that makes Marsala taste like Marsala. It will take a very long time indeed for it to go bad. You could probably keep it sealed and refrigerated for at least a month, probably longer.
I'm sure that I'll get flak for saying this, but.... keep the bottle well sealed standing upright on your fridge door shelf. In the fridge, it'll last a *long* time before "going bad", like sherry. I use quotation marks, because it won't go off the way table wine does. It will lose some of its complexity, and will be a less pleasant beverage, as it ages in the fridge, but I'd say that you're good for a few months, at least. Another suggestion is to experiment beyond veal marsala. I love zabaglione, and have used marsala (granted, not dry) in rice puddings and pound cakes. You could use it to deglaze a roasting pan for jus, or in a gravy. Sprinkle it with some fine sugar over berries. A pleasant preprandial cocktail is marsala, a spritz of soda water, and a twist of lemon. You should be finished the bottle in under two weeks, with all those suggestions! Cin cin!