Let alone that most routers, if not all of them, keep an internal MAC mapping, so that they tend to (well, they actually simply DO) (re)assign the very same IP to the very same MAC address.
The lease (resource consuming???) timer is a nonsense; there is no such thing, When it expires, you just need to disconnect and reconnect (and it's getting done behind the scenes, usually). You can always disable it, too, on the router.
My machines are up at an average of 3 months, with peaks of 1 year...); they never lose a link...
(yes, I am on Linux, but this should apply everywhere)