Well, I don't have kids going through ketchup at alarming rates so I can tell you--ketchup can go rancid and separate if it sits out a week or so in hot summer temperatures. Restaurants go through a lot of ketchup and refill their bottles every night, if not more often.
While we're on the subject of condiments here is a quick and easy sauce that can substitute for remoulade sauce, salad dressing or is great just for dipping. Put about 1 cup mayonnaise (or more if you want to make more sauce) into a bowl. Squirt Heinz Ketchup (red only) into the bowl until the mixture is a rich pink color. Crush 4 or 5 cloves of fresh garlic and stir into the mixture.