I agree. From what I understand, the response game expects is automatically generated.
If it were user generated, maybe the time outs would be scarcer.
However, I suspect that the problem is in the exception handling. The problem occurs if the game disconnects after the initial response. In that case, even if the user pushed the button that he is present,and then disconnects, the match would continue.
One thing I propose is to reduce the countdown. Two minutes is too long. Game usually stops counting at 1:02 anyway. And since the new update, usually when the counter goes below that point, it means that I am disonnected and that the match has already begun without me. The wating for the opponent screen should not be longer than 30 seconds IMO.