Tom, I use iScore and it's good for most of what you say. Definitely stable -- I've never had a problem on my iPad -- and it has provisions for the DP/Flex. You can set it up specifically for softball scoring, which helps.
I only see two drawbacks. One is that if you want to change, say, an error to hit in the third inning and the game is over, you have to undo everything entered up until that point to make the change. When you're done, you have to re-enter all the information, which means you'll probably miss out on some two-strike foul balls and such. That part is kind of a pain, and can be time-consuming.
The other is when you have something unusual happen. It's pretty intuitive for normal plays - you don't have to know anything about keeping a paper scorebook to operate it. But if you have something weird happen, such as an error on a fly ball to right that leads to a bad throw to second that results in the left fielder tracking down the ball and throwing out a runner at home, it gets a little tougher to do in real time. I imagine with more experience it gets easier. But unlike with a paper scorebook you can't just skip that play and then fill it in between pitches to the next batter. You have to resolve it before you can move on.
Sure is nice to have all the stats put together for you at the end, though.