that second paragraph.... waaa??????
Big issue in live chess

Firstly, there is a little exploit players have been making use of in longer time controls. When they're losing, they stall, disconnect and reconnect. They do this repeatedly to trigger a bug on their opponent's end. They'll then make a move, but the opponent's screen won't update unless they refresh the browser. Next thing you know, the game is abandoned. They're exploiting an old and well known bug associated with poor network connections, and I know they're doing it purposely because the network interruptions only begin when they're losing.
Second is a bug regarding piece movement. If you've been winning a couple of games in a row in speed chess, every now and again a piece flies off to a square just beyond where you've placed it. I know it's not just my finger that's slipped because the animation gets weird, as if it recognizes that the piece has been placed but it still continues to misplace the piece afterwards.
Your opponent can't impact your connection at all.
Your connection --> Internet --> Chess.com Live Server
The server takes your move information, calculates the clock times and sends it to your opponent.
Chess.com Live server --> Internet --> Opponent
Nothing your opponent does will have an impact on your connection since only the move, clock updates and any chat are sent to you and all that traffic flows through the live server.

Thanks for the quick response, @Martin_Stahl.
They're not affecting my connection, they're inadvertently messing with my browser - or something along those lines. To understand this, and to determine whether I'm right or wrong, you must first recall the reports of players who claimed their games were aborted while they were waiting for the opponent to make a move. Members responded to this by refreshing their browser's regularly, and it was presumed that the issue was with faulty network connections. I went through this myself. Maybe it has something to do with packets being lost.
My opponent is stalling, disconnecting and reconnecting, in order to mess with something. The result, my browser doesn't update the clock and board. Luckily I usually refresh my browser when things seem dodgy.
Firstly, there is a little exploit players have been making use of in longer time controls. When they're losing, they stall, disconnect and reconnect. They do this repeatedly to trigger a bug on their opponent's end. They'll then make a move, but the opponent's screen won't update unless they refresh the browser. Next thing you know, the game is abandoned. They're exploiting an old and well known bug associated with poor network connections, and I know they're doing it purposely because the network interruptions only begin when they're losing.
Second is a bug regarding piece movement. If you've been winning a couple of games in a row in speed chess, every now and again a piece flies off to a square just beyond where you've placed it. I know it's not just my finger that's slipped because the animation gets weird, as if it recognizes that the piece has been placed but it still continues to misplace the piece afterwards.