People will often refresh/reload if their opponent isn't moving to make sure they haven't actually disconnected. That could be what you are seeing. Or it is possible they have a poor connection or you are having a problem that makes it look like they are disconnecting when your client actually is.
https://support.chess.com/customer/en/portal/articles/1444918-my-internet-connection-is-fine---why-am-i-getting-disconnects-
it is disconnects, then when i come back after a lenghty time....and my opponent disconects numerous times. After the game chess.com restricts my play!! what gives?? i think there is a spam!!