My database table doesn't appear online
Hard to answer but maybe you have data in the Sandbox mode and you haven't synced it to Live? The Sandbox data is only viewable in Preview mode and in Published mode the Live data is visible.
Go to Data Collection, click the Sync menu item and choose to copy all items to Live. Then try again.
If that doesn't do it, check permissions on your Data Collection that all people can read.
Andreas is right. Many times the syncing (or the lack of it if you will.) between the sandbox mode and the live mode of a database is the reason of missing data from the published site.
But, if you try to sync it and still face issues, please post here a link to your site and we'll be glad to look into it and make sure you get a solution. :)
Best of luck!