Ha, sorry about that.
I updated the IP Address to 192.168.0.31
and left the subnet mask at 255.255.255.0 and the gateway at 192.168.0.1
but alas, same behavior as before. I can find the printer right when I start up the printer, but 20 minutes later (even if the printer shows ready and is not asleep) I cannot find the printer on the iPhone.