In the case of the fail-over to the secondary system, typically, the URL to which clients connect, changes.

This can be avoided with the DNS control. In such case, during the fail-over, you can assign the server name to another IP, i.e. to continue to use the name of the primary server, but attached to the secondary server IP address.

Caveat

This may fail on the clients which cached the DNS address. To resolve it, use ipconfig flushdns.