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1.
1. Make an error; miss an opportunity; fail.

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 #2: You can trust me.

MAN #1: I don't know. Everytime I depend on you, you drop the ball.
by Mr. Terrence L. Trezvant November 19, 2006
 
2.
Make an error; miss an opportunity; similar to pull a cootsie.

- This expression comes from sports where a player who fails to catch a ball is charged with an error.
"He'll drop the ball, if he turns down their offer."
by McBang November 07, 2006