Is this in the YouTube Android app (so you are not in XBMC at the time), or the add-on for XBMC/Kodi?
If this is from the YouTube Android app, I've not found any references to auto-repeating videos in the app's options. I've just played a video from start to end and didn't get an auto-repeat option. If it was the Android app behaving like this, try making sure you've got the latest version, use the Play Store app to check for updates, see
https://droidbox.co.uk/blog/googles-play-store-signing-in-and-auto-updates/
If it is in XBMC, head to the System menu and click it, then Video, then the Playback entry. Make sure the Play the next video automatically option isn't enabled. I can't see any add-on options for YouTube that directly relate to this sort of problem. Ah, just tried it myself, I see what you mean! Not sure what to suggest, can anyone else come up with something? I saw
http://forum.kodi.tv/showthread.php?tid=77528 but that refers to playlists in general, and may be Frodo-specific.