An orchestra plays in harmony as long as the conductor is quick. In young mice, the brain receives a signal about food and almost immediately triggers drinking. In old mice, this conductor slows down: after eating, they start drinking not after 4 minutes, as young mice do, but after 21 minutes. That's why they often go around dehydrated even though water is right there.
It all comes down to how the body holds onto water. Old mice have less water and more dissolved substances in their blood, and the hormone that tells the kidneys to conserve water is produced less effectively. On top of that, the kidneys respond to it less well, so water leaves in the urine too easily.
But here's the surprising part: if old mice are deprived of water for a day, they drink more than young mice and enjoy the water more. So their thirst itself hasn't disappeared; it has even intensified. It's just that the signals from the mouth and intestines that say "time to drink after a meal" have become slower. Meanwhile, the signals from the blood that say "you're dehydrated" work as before or even louder. So old mice forget to drink on time, but when they finally get to water, they drink greedily. For humans, this means that older adults should be offered water more often, especially after meals, when the link between eating and drinking is weakened.
Old mice often drop and scatter their food, so to eat the same amount they need to fuss with the pellets longer. This does not prevent them from eating normally, but it delays the start of drinking after a meal.
Not published on arXiv. Here are its page, the PDF and the formalization: you can check it yourself, not only read our account.