To check if the service requires restarting, you can check your system tray. A notification should pop up notifying you. If you don't see that, you can hover your mouse over the Leap Motion Control Panel icon and the text that appears should let you know if the service isn't running.
It's possible that the service is crashing. If you haven't already, try uninstalling the Leap Motion software and do a fresh installation to see if that resolves the issue for you.
If the issue persists, please check c:\programdata\leap motion\ and send over the .dmp file(s) that were generated when the service crashed for you. If you see multiple .dmp files, send over the most recent one.