My connection isn't that good, therefore it's usual for me to disconnect and then connect again to Live Chess during a game at least a couple times... I'm not doing it intentionally, but this message keeps apearing: "Please do not intentionally abort or disconnect from games, or make your opponents wait unnecessarily. Your account may be restricted if you do not follow our Fair Play Policy. Thank you for keeping Chess.com a fun and fair place to enjoy chess!" Moreover sometimes I stay thinking for 4 or 5 min becouse I think it's a needed stuff for the current position, I'm not wishing to bug my opponent.

Should I be worried about this or it's okay once I'm not doing anything wrong?

Problem is that chess.com cannot be sure that you're not disconnecting deliberately to avoid defeat. I'd suggest that on-line chess may be more appropriate or you. That way, you're disconnection problems and yor natural need to think about your next move will be sorted.

WHEN YOU DISCONNECT AND YOUR TIME RUNS OUT YOU LOSE OR YOU AVOID IT AND THERE IS NO RESULT?

People try to avoid defeat by disconnecting and reconnecting later in the hope their opponent has abandoned.

This makes me believe the point is how much time a player keeps disconnected. Then once the connection is recovered whithout delay there shouldn't be no problem, right? 

Right...reconnection within a certain amount of time doesnt lose u the game

wbilfc, by this I was meaning no need to receive Fair Play Policy warning if the connection is lost and then recovered in a few seconds... Even if it happens lots of times during a game.

Agreed :0)