Security analysis of this one time password based scheme for copy protection
Is the motivation for this a copy protection scheme? 

If so, the most obvious problem is that if $K[n]$ is transmitted by the server but not received by the client, then synchronisation is lost.

This could happen if there is a proxy in between as is often the case in corporate networks with HTTP (or more controversially HTTPS) traffic. The updated value could be transmitted to the proxy but not downstream to the client. At this point, the application is irreparably broken.

Is this one-time password being transmitted over a secure channel? If not, then the following problems also apply:

How does the client authenticate that the $K[n]$ really came from your server and not someone else?

How does the server authenticate that the $K[n]$ provided to it, came from the client and not some third party?

If the one-time password is used to authenticate a message came from a valid host, how do I stop the message being modified in transit?