I've been having the same problem since March 21, 2012. I have WordPress 3.5.1, and Jetpack 2.2.1
I have done the Jetpack suggestion of X out facebook, go to facebook, take out the wordpress app approval, go back to Jetpack and add a new facebook connection.
When I create a post, I click on the "Publicize: Edit" and see that the Facebook box is checked.
After uploading/publishing the post, nothing is updated to facebook. I go back to my post, and click on the "Publicize: Edit" and now the Facebook box is UNCHECKED.
I go to Jetpack-publicize-configuire, click on add new facebook connection, and the radio button is unchecked. If I check/select the radio button, click OK, and save. Then I go back and the radio button is still unchecked.
It has to be a bug with Jetpack that is not saving the selections, and thus unable to publicize when uploading/publishing a post.
Any ideas of a work-around?