What your describing can be a connection related issue. The site has some automated processes in place to detect things like that already.
That said, discussions of cheating, potential cheating, or cheat detection are not allowed in the general forums. If you really think any member is using disallowed resources, you should report them directly to staff and now publicly accuse them.
https://support.chess.com/en/articles/8562517-how-do-i-report-someone
If you like to discuss the issue, in more general, join the following club. https://support.chess.com/en/articles/8562517-how-do-i-report-someone
I played against someone who kept leaving and coming back. Profile [removed -- MS]. I think he or she was cheating. It has been so hard to play a fair game. What is the deal with this? Can we just kick out anyone who keeps leaving the game screen?