As long as it remains somewhat warm, recooking is permissible. For solids this definition works, but for liquids we need some other criterion.
Water is both a place or medium within which something gets cooked, and a cooking agent.
Liquids are not only cooked by fire, but they also become a partner with fire to act as a cooking agent. A liquid, though, is an active participant in cooking the food which is in the pot with it. It is heated by the fire below it, but then it becomes that which cooks the meat, fish, or vegetables in its midst in a way which the fire itself would not have been able to. To cook a liquid, say the Tosafot, is to turn it into a cooking agent. Once a liquid has cooled down, it ceases to function as such, but it will resume its role if reheated.