Usually what happens in this case is the rebate people mix up the ship date with the order date.
That has happened to me on multiple occasions... even after highlighting the correct date.... x.x
What I usually do is call them up (the number should be on the postcard) and if this is from rebatehq.com (or some place in miami, FL) what you need to do is hold on the line even after they tell you the options. Once you wait for a bit they would say "Please hold for the next available representative" and you get a live person. Usually all the other options are dead ends.
Note: You might have to make one or two calls to figure out where to wait a bit.
When you do get a hold of someone, they would ask for the tracking number, which is listed on the postcard. They will tell you why you were rejected (basically reading the postcard) and what you need to tell them is the order date was within the promotional period and its possible that it was confused with something else. A lot of the rebate companies have records of the receipts they receive, and they would verify it right there and correct it.
What is important is is that you are DESERVING your rebate so you shouldnt give up. Be polite and confident. Worst case scenario is that theyll ask you to fax or mail in your receipt.
Now, if you dont have your receipt handy, hopefully you ordered this product online. If you have, you can print an order history somewhere, and most rebate companies accept this as well.
Good luck!