There's nothing from the site that could cause a complete loss of Internet.
There are things you can do to minimize issues between you and the site but what you're describing is unlikely to be helped by them unless you're somehow maxing out your router while playing on site
https://support.chess.com/article/4720-online-chess-performance-optimizations
I have made a post similar to this before regarding Chess.com and my internet but I have had enough. Back In February, whenever I was playing rapid (and ONLY rapid, not blitz nor bullet) and had low time, I would get disconnected from my internet ENTIRELY. I couldn't enter any websites for a few minutes, causing me to resign from the game and get reported for "abandoning" matches. This happened several times forcing me to lose tons of elo. All of a sudden, I never had this issue in March but then suddenly the issue arrived on April 1st again and I dropped from 2040 elo to 1980 elo (I have gone back to 2017 as of writing this). I have never had this happen when losing or when I have plenty of time and I KNOW IT. People have told me that I only notice it when low on time and winning and not notice it when up time or lopsing but that is false because I tested this theory multiple times and it was wrong. Now, before anyone comes and says that I should check my internet connection, they should know that this ONLY happens in chess.com and it only affects MY computer which disqualifies so many things. The only possibility I have come up with is that there is an error between My computer and Chess.com servers which leads to the removal of my internet. I have also cleared cookies and cache but I have not tested another web browser. Currently I use google chrome which I am unsure if its good. Last thing I want to point out is that In february and April, I have reached a new milestone and those were coincidently the months where my internet was getting removed from my computer. If anyone can help please let me know as I am studying a lot at this time.