James,
Check and make sure of a few things:
1) In the Configuration -> Facebook API tab, make sure that "publish_stream" is added as an Additional Required Permission. If that's not being requested, it would explain why you can't post. It's possible your other user granted that permission previously (months ago), and that's why he can post.
2) When you post in JomSocial, make sure the status update is set to "Public". If it's anything other than public, JFBConnect won't post that to the FB wall for privacy reasons.
3) To full re-test, go into Facebook.com and then your "Account Settings" area. Hit the "Apps" tab and remove your application there. Then, login again. It will re-request all the permissions. Make sure the Post to Wall permission (in a separate popup) is being requested and test again.
Hopefully one of those gets you going, but if not, let us know.
Thanks,
Alex