Your router probably assigns LAN IPs dynamically. You can usually change this behaviour by assigning IPs to MAC addresses in the router config. Each network card has a (pseudo-unique) address called a MAC. You can use this to give your machines static IPs.
Your router should list the MAC addresses for each of the computers connected. If it doesn't, you can get it from Miami's hardware "SANA-II Perameters" window by pressing the Query Device button. On the PC you can get the MAC address by using ipconfig /all or in an MS-DOS window or running winipconfig (not win2000 or XP).
This explains it a bit better.
Then, you can set up the LAN IPs as the following (for example):
192.168.2.1 Amiga
192.168.2.2 PC
Then you go into Miami/Genesis, go to the Database, and add these under Hosts. You'll know it works when you can do
MiamiPing PC
or
MiamiPing 192.168.2.2
from the Amiga and it works. It should work from the PC too.
If your router can't assign IPs by MAC, then you'll probably have to turn off DHCP and connect to it using static IPs. This isn't hard at all, but you should check your router first.