I'm assuming you use a flat IP address space with no interior routing. Without WINS, each of your machines must broadcast to find Windows resources and to resolve the NetBIOS names of the servers hosting those resources into IP addresses. The timeouts involved with those broadcasts are fairly long but not indefinite. You can easily saturate a network with 30 or more clients broadcasting for all their resources.
I would advise that you install WINS on your PDC (not the multihomed member server) and configure your clients to point at this WINS server. Yes, I know that's a pain because you use static mappings, but give it a try just to see.
You might have a problem with the PDC. The server must respond fairly quickly to logon requests. Do you have any suspicious Event Log entries from NETLOGON or any server services?
Don't rule out infrastructure problems. Do you use a shared media hub or a switch for your clients? Do you experience other connectivity problems? If none of this works, write back with the results of your testing.
Dig deeper on Domain Name System (DNS)
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