Some kinds of Facebook connection issues can be resolved by simply logging out and logging back in to Facebook through Sonlet.
Head on over to your Inventory page and scroll down to the Facebook posting area. You should see a blue Facebook "Log Out" button:
Click the Log Out button.
Once you've done that the button should turn into a "Log In" button:
Click "Log In" and click through the screens asking for permission to post publicly to Facebook on your behalf. Make sure that when it asks you "Who can see Sonlet's posts on your Timeline" that you answer "Public". If you select "Friends" then only your Facebook friends will be able to see your pictures posted by Sonlet.
After logging in the button should turn back in to a Log Out button and you should be back in business!