A few years ago, YouTube switched to a streaming protocol called Dynamic Adaptive Streaming over HTTP, or DASH for short. While it's more efficient in most cases, it means you can only ever preload the video a few seconds ahead of your current position, no matter how fast your connection is. Luckily, it's easy to disable.
First, you'll need to add YouTube Center to your browser of choice, either as an extension or as a user script. Once that's done, you'll notice a gear icon in the upper right corner of YouTube. From this dropdown menu, go to YouTube Center Settings > Player, and uncheck Dash Playback. Now, YouTube videos will be able to preload in their entirety, which is awesome if you're on a slow connection, or if you're jumping around from point to point.
YouTube Center obviously has a lot else going on, so be sure to poke around once you've cured this particular grievance.