A.  By “dropped the ball”, you can be referring to two different situations.  First, it was your company who messed up.  Your company didn’t fulfill the promises you made.  Or, second, it was you, personally.  You didn’t do what you said you would do, or you somehow personally violated the customer’s expectations for you.  Regardless, the remedy is similar.
            You must make a personal, heartfelt and detailed apology, as soon as possible.  And you must do that to everyone who is impacted by the problem.  If the problem was your company, apologize on behalf of the company.  If the problem was you, personally apologize.
            You do that first, because that eases the tension in the situation and acknowledges the impact on the customer.  Remember, you are building a relationship with these people, and, as in all relationships, sometimes things don’t go quite right.  An apology is a great way to clear the air.  Most people will tend to accept your apology and not hold it against you.  Everyone makes mistakes.
            Now comes the hard part.  While most people will accept your apology, they won’t necessarily forget the infraction.  It’s like catching one of your teenagers smoking dope.  He may ask for your forgiveness, and you may give it, but it is prudent for you to watch him carefully for the next few years.  You can forgive, but you are wise to not forget.
            Same thing with your customers.  It’s one thing to forgive, it’s another to forget.  They won’t forget quickly or easily.  So you have to earn their trust back by your actions, not your words.  You’ve got to consistently do what you say you are going to do.  Your company must, time after time, do what you say they will do.         
             Regaining trust is, in most cases, a long term project.  It’s much easer to lose a customer’s trust than it is to gain it.  Your actions, consistent and reliable, backed up by your heartfelt interest in the customer, will, over time, win them back.