That sounds more like you got disconnected. The game stats show you as abandoning, which is what it would show if you got disconnected.
My opponent abandoned the game and I lost...

My connection showed four bars the entire time and the a6 move registered when I made it. The site said he left the game as well.

Sometimes the client incorrectly states it when it gets disconnected. I've seen in happen before on games. When you get disconnected, your move may still show on the client until either it reconnects and it will reset to before the move or you eventually get the loss dialog due to abandonment.
If you are on the website, there are some things you can do to potentially improve the connection and limit the issue:
https://support.chess.com/customer/en/portal/articles/1444918-my-internet-connection-is-fine---why-am-i-getting-disconnects-
https://www.chess.com/blog/News/how-to-adjust-your-live-chess-connection
I was playing a game of 10min blitz and my opponent disconnected after I made a move. The timers started to flash and after one minute it said I lost due to resignation. This is very annoying.
I pasted the game where it happened, and I don't think my opponent cheated in any way to create this error. I'm black, and I played a6 on the next move when this all happened.