By default settings, there isn't a ball save feature/timer in TAF. It isn't like many other games that give you a ball save timer. If there is such a setting, I've never seen a game set that way in over 20 years of playing TAF. I suppose it's possible, right?
There is something else though.
If you launch it and it drains with zero points scored (no time limit at all), then the game believes that it failed to kick the ball into the shooter lane in the first place, and it will then kick another ball into the shooter lane again. If you launch it just short of the skill shot, and it rolls down the field, and you just let it go, you can have another shot at the skill shot (and keep doing it over and over again, as long as no switches/points are hit). So a good strategy is that it is better to miss "short" instead of "long" if you are going to go for the skill shot. Of course it won't work if you are SO short that the ball goes back into the swamp instead of out the end of the shooter lane. That's because the switch will get hit inside of the swamp.
The shoot again light, is just an indicator that you have scored an extra ball, which will be played after it drains. Go ahead, he's got a whole bucket full.
But then again, I suppose there might be setting that isn't documented... and I've just never seen it!