I am guessing that you just disconnect the machine and move it, without powering off ? I am also assumeing that the switches are configured correctly for the forwarding-address to the correct DHCP server,a nd that the scopes are correct on those DHCP servers.
If you move the machine, and do the following commands at a DOS prompt, does it then pick up the correct IP address ?
If it does, then the issue is that the machine is keeping it’s old address, rather than it getting the same one from the DHCP server. If you regularly move machines, then you may need to set the lease time down quite low. the disadvantage is that there is a lot more DHCP activity, which eats into the bandwidth, and ,makes the DHCP server work a lot harder.
You should really release the old address before moving the machine, then it will try to get a new one when reconnected elsewhere.
Hope that worked for you.