Network routers have a different design purpose in that it is their job to look out for new connection and to assign IP address.
The PLC fimware initializes the Ethernet parameters during startup and most often the PLC is assigned a fixed IP address during the initialization so that will be the parameter it uses. If the fixed IP address has changed then it require a reboot in order to re-initialize the Ethernet port.
The PLC firmware does not want to spend precious CPU time to periodically check to see if it has if the IP address has changed in order to re-initialize the Ethernet port.
In many applications the PLC may not even be connecting the Ethernet port to the network, hence it is by design that the PLC only check for DHCP IP address (if IP address is set to 0.0.0.0 for Fx based PLC only) during boot up and if it doesn't find an address it assume that there is no network connection or no DHCP server and thus would ignore the Ethernet port.