multiple domains with NT workstations

My company has three domains Like Domain_A, Domain_B, and Domain_C running UNIX servers. I have problems with it for multiple clients. 20 clients are Windows NT/98/2000.
My problem is many of these 20 clients need to log on to different domains. For instance, Client_1 has the priviledge to access to Domain_A and Domain_B. Client_2 or Client_x has similar situations. Now if a client is logged into Domain_A, and then to Domain_B, and then back to Domain_A, the client’s username and password is no longer valid for Domain_A. I wonder how this could happen and how I could resolve.

Your help is greatly appreciate.

Thanks a ton.