So you need to understand how IP address are given out, ie DHCP. "The Dynamic Host Configuration Protocol (
DHCP) is a network management protocol used on Internet Protocol networks whereby a
DHCP server dynamically assigns an IP address and other network configuration parameters to each device on a network so they can communicate with other IP networks.":
https://en.wikipedia.org/wiki/Dynamic_Host_Configuration_Protocol
The information given out by a DHCP server, which includes the IP address is valid for a limited time set by the DHCP server administrator. After that time period, the DHCP server will 'release' the information and it has to be re-requested. Now, generally as soon as a device loses its reservation (or when the reservation time is about to end), the device will immediately send a request. Because of the speed of this cancellation and renewal, most of the times the IP address will be the same. And most DHCP servers use caching, so a lot of times the same address is re-issued even after a period of hours as long as the MAC address doesn't change.
Knowing this, there is always a chance that an IP address that loses its reservation will not be reissued to a client because it is assigned to someone else before the client renews it. It is rare because of the near instantaneous cancellation and renewal requests, but it can happen.
Now, I mentioned MAC address before. The MAC address on every ethernet device is what uniquely identifies that client to the DHCP server. The DHCP server uses that MAC address to know what device has what IP address. If for some reason that MAC address changes, like when someone purchases a new router (which has a different MAC address than the old one), the IP address given out by the DHCP server can change. This is why routers have a 'MAC clone' feature that will allow you to set the MAC address being reported to the DHCP server in order to preserve the current IP address.
The third way I've found that DHCP IP address change is when an isp has an infrastructure change such as changing head-end equipment or rearranging networks. Then they may change DHCP pools, or completely re-route traffic so that your device is not connecting inside their network where it once was. In that case, when the reservation ends and your device sends its request, you will get a new IP, even if you were connected continuously.
I have some permanent networks that are based on DHCP IP addresses (IPsec site-to-site vpn tunnels). This is usually not done using DHCP addresses because of the fact that DHCP IP addresses can change. However, in my experience the only times I've had to reconfigure these networks for an IP change has been in the above scenarios, and that's been like 3 times in the last 7 years. If your device is on 24x7 and your isp isn't growing/shrinking/upgradeing/etc, the likelihood of your IP changing is very slim.
Hope this tells you everything you wanted to know!