In order to prevent users from switching off LogMeIn from the systray icon, you must have a paid subscription to LogMeIn Central and the LogMeIn Control Panel installed on the host computer.
You can disable this feature through a Host Preference Package. Once the package has been created and the computer added to the package, please go to Edit Host Preference Package and the Access Control category. From there, uncheck the box next to "Allow the user to turn off LogMeIn." Make sure to click Save when you are finished.