It's not done it before on other videos only this one?Generally youtube memorizes the last spot you left off. Try watching until the end and then try to rewatch it after?
I tried it on my iphone and MacBook I'm going to try it on my mums laptopIt could be your browser, have you tried in another or on your mobile phone etc?
It seemed to be ok when I tried it on my mums laptop so weirdIt could be something saved with your browser. If it doesn't get fixed, then you should report the problem to YouTube.