This must be a joke, right? I'm sorry if this comes off as rude, but is every one of your opponents supposed to adjust their play time to your schedule? If you don't have time to play the game, don't play the game. If we matched up and you were away so long that the timer actually expired, I'm clicking that forfeit button and attempting to match up with someone who won't waste my time.
There was about a 2-3 month period over the summer where I knew I was too sick to make it through a 9 inning game without needing to pause for an extended period of time. Do you know what I did? I stuck to 3-inning game modes where I was more likely to make it through without needing to pause, or I played conquest/moments until I was sure I could actually get through a game without wasting my opponents time, or risking a forfeit.
If SDS actually instituted what you're suggesting, as soon as anyone went down by a run or two they would just pause the game indefinitely and wait for their opponent to quit out of frustration. This idea is so incredibly bad that I am convinced it must be a troll post.