If your Rpi is on the network with a static IP, it never talks to the router to 'advertise' itself.
A really simple solution is to use the upnpc program (in miniupnpc package) to set your port forwarding dynamically. MUCH easier than tweaking the router all the time.
You'll need upnp enabled on your router, usual caveats apply here.
The following command will forward internet port 1337 to internal port 22 on the server:
upnpc -e "ssh server" -a $(hostname --all-ip-addresses) 22 1337 tcp
See the man page for upnpc of course for more details, but here you can see
-e sets the name of the forward setting,
-a lists the server's IP addresses, the last three items are inside port, outside port, type of connection (tcp/udp).
I use a similar command to forward port 80 from outside to my own web server too, don't have to set up a DMZ with all that that entails security-wise. (and no, I didn't put my actual external ssh port number here... duh!)
Another method would be to set a static DHCP setting for your Rpi in the router, and shift your Rpi back to dynamic IP (DHCP) mode... but unless you're going to also set up some sort of name-server system, this gets hairy fast since your RPi address COULD change. (Yes, I know it's not supposed to... )
Letting it set up its own forwarding using its current IP address is the best way, as it adapts as needed.