If your posts say Posted under the Status column of that party, then you can be sure that the system posted them somewhere. If you're not finding those posts on Facebook even after refreshing, you can check and see where the party is scheduled.
To find where they posted:
From your PostMyParty dashboard, click Parties.
Then, click on the name of the scheduled party you want to check.
The type will tell you whether you've scheduled that party to an event, group, or page.
Click the highlighted text (Link to Personal Group / Event / Page), and a new page will open to the Facebook location you have scheduled those posts to.
The posts you're trying to locate should be published to the group/event/page that had opened in this new window.