[Rob]

IP addresses are typically allocated by network servers for a period of time. That can be hours or days. This is often referred to as a lease. Typically servers record details of the device which it communicates with using a mac code. This is an identifier built into the network ports of most network type devices including routers, computer network cards, modems and such like.

If the device remains connected to the network, the lease will be renewed with the same IP. Even if a device is disconnected from a network, if you reconnect before the lease has expired, it will pick up the same IP.