As a rebound, I have tendered the same article to another publication to see if there is a match. I'll have to make a few amendments to meet the readership there but it will be worth it if it gets accepted.
Freelancing requires one to make the best of every hour spent working. The trade off has to be close to perfect, in order to reduce time wasted on assignments that will not generate revenue. This is especially true for those who have very limited time to spend at the writing desk, like me.
The first step after a rejection - I have learned - is to move on to other options immediately. Unless the piece is timeless, obsolescence is news' biggest enemy - unless you can come up with a different spin of a new flavour.
And after moving on to other options, move ON. Get cracking on the next big idea, the next great project or the next weekly assignment. A rejection is not the end of the world - it provides an opportunity for better focus, especially after learning from that one mistake.