Why is Drupal deleting my images?
I'm not familiar with the One-Click Upload module, but you might want to check the file_usage table after adding an image to see if it's recording a usage. If it's not recording a usage, it's being deleted because on cron run, Drupal automatically deletes files from file_managed that don't have a usage recorded in file_usage.

Drupal does not detect linking from entities other than the one(s) on which a usage was originally recorded. For example, if you added a link to an image in the markup of node 5, but the image was uploaded as an attachment on node 3, the image will disappear when node 3 is deleted, and node 5 will show a broken link.

If this is your problem, you could solve it by using the File Lock module to add file usages so they aren't deleted, or you could switch to the Media module, and apply this patch that has been committed to the latest dev (and that I personally wrote some tests for) to ensure that a usage is being recorded for files uploaded via WYSIWYG.