LegalJob is consistently emphasizing the value of persistence.  That quality will help you overcome rejection throughout law school career, including during the law school application process.

A recent article provides good suggestions and hope for applicants originally denied admission from their dream law school.  The advice is basically to improve your candidacy and then reapply and tell the committee what you have done.  This advice also works down the line, for example, after you are rejected from your dream law firm.

The article is linked here. The three steps discussed are:

1. rework essays
2. retake the LSAT
3. include an addendum with better grades, additional work experience, something else that the committee would possible care about, etc.  

Note that the law school is looking for future donors.  Anything you can say to demonstrate that there is a reasonable chance you will be a future donor could be helpful.  As just one example, if you are focused (based on work experience or undergraduate major or both) on a particular practice area and know that your goal is to work at an AmLaw 100 firm in a big city that is known for that practice area, you would likely fit the bill.