OK... I have:
* A4000 + Mediator + Realtek 8139, MiamiDx
* A1500 + AmigaNET Zorro II, MiamiDx
* AmigaONE XE G4
All attached to a D-Link 10/100 switch, which is attached to an AR-601 ADSL router. ALL 3 machines get their network info via DHCP from the router, and it all works great with no connection problems, or anything. It all just works great.
So... I don't think the problem is with MiamiDx and DHCP per se, but your individual setups.