The YouTube video player is quite unstable in that sense. Sometimes it will reload the video and sometimes it won't (either because the resolution of the video changed, or the cache is full, etc).
If you play the video completely and then go back and watch it again (pressing the replay button), you should be just fine.
Additionally, if this becomes a grave problem, I recommend downloading the videos with the following websites:
(Disclaimer: I'm not affiliated with either of the sites; I'm just suggesting what has worked for me. However, I'm not responsible for the functioning/availability of such services).