I know this question was written over ten years ago, but I was having this same issue last week and worked on it for literally 6 1/2 hours until I finally figured it out, so I thought I better share my discovery in case there is another poor soul out there who has tried every answer on every forum and STILL isn't having any luck.
This is how I got it to work on Microsoft Word 2010, but I would think it's a good option to try on any version of Word.
Backstory - I designed my postcard on the document before creating the mail merge. I had our company logo, a text box with our copy, the address lines that are on most postcards, and text boxes above each line - where I was planning to do the mail merge.
After a long day of torment, searching for answers to no avail, and wanting to throw my computer across the room a billion times, I finally figured out that the text boxes were my problem. Those stinkers! You can't correctly mail merge in text boxes. If you try, it will do crazy things like copy one person's information on all four postcards on the page or not show any entries at all. Note: You can have text boxes on your postcard (for copy and such), but you CANNOT use text boxes for the actual mail merging portion. You have to insert your mail merge items on the ground of the postcard. In other words, you have to do all mail merge activities on the postcard itself instead of adding a text box and inserting the mail merge items in that text box.
When I finally figured this out, I wanted to pop a bottle of champagne and celebrate while simultaneously crawling into a hole, dropping into a fetal position, and not coming out until the Arizona Cardinals win a Super Bowl.
I'm not sure how this will translate across the internet, but I attached an example of what finally worked for me just in case it's useful to anyone.
I sincerely hope this answer helps someone's brain from exploding and then imploding and then exploding again while trying to deal with the beautiful world of mail merging.
GOOD LUCK YOU FIERCE, MAIL MERGING WARRIOR!
-Chloe