We cannot help you until you tell us what method you are using and provide step by step details of exactly what you are doing. Are you using Publicize? http://en.support.wordpress.com/publicize/
1. Log into your WordPress.com blog. Go to your blog’s dashboard -> “My Blogs” -> uncheck “Facebook” under “Publicize”.
(On the “My Blogs” page, make sure you’re looking at the correct row for the blog in question.)
2. Reload the page and confirm that the Facebook checkbox is unchecked.
3. Log into your Facebook account. Go to “Account” (upper right corner) -> “Application Settings”. Remove “WordPress.com” by clicking the “X” in its row. (If there is no WordPress.com row, don’t worry, just skip this step).
4. Log *back* into your WordPress.com blog. Go to your blog’s dashboard -> My Blogs -> *reclick* “Facebook” under “Publicize”.
5. Wait for the popup appear that asks you to “Authorize connection with Facebook”. Click that button.
6. You’ll be taken to Facebook and asked to “Allow” several pieces. Allow them all.
If your are not using Publicize then what method are you using please?