That's usually down to the cache. The cached version will carry on showing unless you clear caches. However, at some point the cache will expire or someone will access a non-cached page and then...
Posted1 day 22 hours ago by Martin Price | System Horizons Ltd (yorkshirepudding) on:
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I recommend the YouTube Field module. It has the option to be responsive and use the full width of whatever container it is in
There's also Video Filter if you are going to paste the videos into the body text.
I also use the "YouTube Field" module where there is a lot of content to embed.
If it's just a one-off... use iframes.