Firstly can I ask which app version you're using? Is it Android or iOS?
After the game starts and (using this one as an example where you play black http://www.chess.com/livechess/game?id=658124388 ) can you tell me what you see on the screen?
Do either of the clocks start?
Do you touch anything on the device at all? (other than the sides to hold it 
)
When you're playing white, do you make a move? Can you describe to me exactly what happens / what you do and see on the app immediately after the game appears on your screen to play?
I've been using the chess.com app, and i lost 12 games in a row because i "resigned" and neither of us had even made a move. That's so stupid. I lost about 80 points because of the stupid app. Please tell me this will get fixed. This is the second time this has happened to me.