What you're looking for is "DHCP" settings in the router. The DHCP (Dynamic Host Configuration Protocol) server is responsible for issuing IP Addresses to any client computer on the network that requests it. By default, most operating systems (Windows inclusive) are configured to find a DHCP server on the network and get a "lease".
Each lease includes an IP for the client to use, various information about services on the network and an expiry date.
The DHCP server has a fixed scope; a range of IP addresses within thin the network (for example 192.168.0.32-254, which is a total of 222 addresses). It can be configured to use nearly every IP address there is (for example, 192.168.0.2-254, which is all but 192.168.0.1 for the server itself), leaving no space for "static" clients (computers that don't ask the DHCP server for an IP, but use a preconfigured one), or it can be configured to issue a narrow range (for example, 192.168.0.200-250). DHCP servers can also be configured to issue specific IP addresses to specific physical network adapters (by the MAC address), allowing a sort of server-side static IP.
DHCP servers are also usually smart enough to give a computer the same lease, if it requests another before the current lease expires.
The main problems that can occur are
- As InstallingIT says; the DHCP server could be trying to issue a lease to an IP address that is not available, because another client on the network has been configured with a "static IP", that is, rather than looking for an IP Address, it uses a fixed one. Since the DHCP server did not issue the IP Address in question, it doesn't know if any other hosts on the network are using it.
- The DHCP server has run out of leases to issue. Usually, leases are good for about a week, before the client must request another. In certain situations though, clients keep asking for new leases and the DHCP server keeping issuing them until it runs out of IP addresses. This can happen with laptops when there is poor communication between the wireless access point and the DHCP server, or where the DHCP server is not smart enough to reissue the same IP address.
The first problem is solved by ensuring that any static clients are outside the DHCP scope. This means ensuring the DHCP server has actually left some space in the network range, and that any static IP addresses are not in it. For example, the DHCP scope could be 192.168.0.100-200, and static bindings could be in the 192.168.0.1-99 range).
The second problem can be resolved by reducing the lease duration to a shorter length of time - perhaps only a few days.
Both solutions require a reboot of the router to ensure all the current leases are invalidated.