I could not open ZoneAlarm by double clicking the icon in the TaskBar Tray or by right clicking on it. When the mouse cursor was over the icon, the message "Protection Is Up, UI is Initializing" appeared.

Start/Settings/Control Panel/Administrative Tools/Event Viewer/System showed multiple Error Messages numbered 7001, the text of which read:

The TrueVector Internet Monitor service depends on the World Wide Web Publishing service which failed to start because of the following error:
The dependency service or group failed to start.

And:

The World Wide Web Publishing service depends on the IIS Admin service which failed to start because of the following error:
The service cannot be started, either because it is disabled or because it has no enabled devices associated with it.

I started the IIS Admin Service and the World Wide Web Publishing Service and ZoneAlarm started working normally and the message "Protection Is Up, UI is Initializing" was no longer there when the mouse cursor hovered over the ZA icon on the TaskBar Tray.

I did not even have to re-boot.

I realize this is not a global solution for all occurences of the "Protection Is Up, UI is Initializing" message, but it is worth checking the Event Viewer first.