The Video Resumer add-on will automatically resume YouTube videos from where you played them last. Without this extension, for example, when you click through YouTube videos, back and forth, they always start from the beginning. No more. With this extension, previously seen videos will resume from where you left them at. Even if you restart your browser.
I have noticed myself that YouTube will do this on it’s own from time to time. Not sure what the exact rules are (perhaps if you have not watched another video on that person’s channel?) but this add-on for Firefox will make sure you can resume your watching 24/7.
You can pick up the Video Resumer add-on for Firefox from the Firefox Add-ons website.