2. To make a mistake, especially by doing something in a stupid or careless way.
3. To fail to keep working to reach a goal.
This expression comes from the game of FOOTBALL, where it's not a good thing to drop the ball when the ball is in play. It's mainly used based on failure and mistakes. So, if you want to tell someone how important it is to succeed in a particular activity, then this is a good expression to use.
MAN #1: I don't know. Everytime I depend on you, you drop the ball.