Hi Brittany,
There are a few factors involved that could affect the scheduled publish post time. First, make sure your date/time zone in Joomla's Global Configuration and your server's php.ini file corresponds to your intended time zone. Secondly, I suspect you do not have cronjob set up to improve the efficiency of scheduled posting.
If you have these set up correctly, we still need your backend, ftp, social media, and cpanel access so we can perform an investigation and tests regarding your issue.
Can you provide us those details at
http://stackideas.com/dashboard/site so we can help you out with this? Let us know, thanks.