Finesse is not connected to the CTI server. Make sure there is network connectivity between Finesse and the CTI server. Then sign in to the Cisco Finesse Administration Console and verify that the settings in the Server Settings gadget are correct.
The DNS was not configured during the installation. To check if DNS was configured during installation, check the install.log for the following:
InstallWizard|USER_ACTION_BTN_PUSH: Screen = DNS Client Configuration, button pushed = No|<LVL::Info
Try to sign in to the desktop on the alternate Finesse server. If Finesse goes out of service after the agent is already signed in, the browser is automatically directed to the desktop on the alternate Finesse server.