The fact that you are "on mobile data" and wifi doesn't mean that your connection is continuously strong. I would stick with one or the other.
If you are staying in one place, there's no reason for a stable connection to be switching back and forth between wifi and mobile data. That only happens if both connection methods are relatively weak and you are moving.
Are you playing while you commute?
Your phone probably tries to use wifi if available (to save you money) and it may be switching back and forth between the two and adding and dropping the connection many times.
Also, loading the ads that you get in the free version of chess.com takes most of the bandwidth you are using.
The fact that you only drop your connection occasionally while you are mobile is pretty remarkable.
In almost all my games, either my game or my opponent's game alerts that the game will auto-abort. It drives me crazy because it happens when I'm on mobile data, and also in wi-fi. My internet connectivity is strong on both, but the 1 out of 5 games or so will drop. To make matters worse, I get the alert at the beginning of my games not to make players wait and not to leave gsmes6. Are they kidding? I'm not doing anything wrong, my connection is strong, and I get threatened not to let the games drop. It's extremely frustrating, especially if they can actually look at the games that drop and see that I was 1 or 2 moves away from mate (or winning at the very least). I'm ready to stop using chess.com altogether; I also use another site which has unlimited free training and I've never had a game drop. I like Chess.com because I think there are more players available for blitz play. Any suggestions?