When you merge you can only have one card on your screen.
If you are relying on the print preview in Publisher 2002-03 this is a Publisher
bug. It will show all 4 cards the same. If you are unsure print a test. There is
an option for a test print on the print page.
If you are using 2007, File, print merge, be certain to select multiple pages
per sheet.

After much frustration, I have the same problem.  I am using Word
2007....here is how I FINALLY got it to work.

Start from scratch with a blank document
Go to mailings
Start Mail Merge
Select Labels and choose one like Avery 3380 which is 4 to a page.
Click OK
Select your recipients and edit them accordingly.
Insert your merge fields....you can copy and paste from one post card to
another.
You may notice it says <<next record>> DON"T Delete this..there should be
one on each postcard except the first postcard.
Once you have you merge fields on each postcard...and yes, they will look
the same....put your mouse on the <<Next Record>> field and RIGHT
click....choose the "update field" option and notice all 4 postcards will
have different addresses.
Ta DAH!

Best of luck to you!  Lori