If the DHCP lease has expired while the device is off or asleep it may or may not get the same IP when it reconnects depending on the settings on your router. If the machine is on when the lease expires it can typically renew the lease and retain the same IP. Generally DHCP leases default to 1440 minutes (24 hours).

Best practice is to do what I mentioned before and have your router reserve the IP so if the settings on your device get reset for some reason you won’t have to go hunting the IP. At least though, you should have a range of IPs outside your lease pool so you can assign static IPs on the device without running into a DHCP conflict, but this runs into the aforementioned issue of the device forgetting its settings.

That seems like a problem with the router.

Not entirely. The lease default is usually about 24 hours, that computer would need to be completely offline for a day and the IP address would usually need to be reassigned before the device gets a new IP. Even then, the router would probably try to give it the same.