If the client isn't sending the update, it's not getting to the server so server troubleshooting will be useless.
Likewise, if the server is receiving the update but the record is still not getting updated then it might be a dns Node object permission problem. If you need help, this Technet article is a great resource we'd recommend for understanding the entire workflow from client to server.
If you move a DNS server to a new subnet, you may have to reconfigure every client computer.
If you move a client computer to a new subnet, you may have to update its IP address.
Feel free to refer to this blog post for more information on the script and how to use it.
When integrated with AD, DNS records are just AD objects.
To successfully update, the AD computer account needs to have Modify rights to its own dns Node AD object.
The designers of TCP/IP wanted an identification scheme that was independent of any one computer or network equipment design, so they established a scheme of IP addresses.
If you've ever surfed the Web, you have probably seen IP addresses at one time or another (numbers such as 192.168.144.77).
If it's started, ensure there's no events in the computer's System event log that indicate a problem. Check the advanced DNS client NIC setting The "Register this connection's addresses in DNS" should be on by default, but we've seen instances where it's disabled through some kind of policy.