Every couple of days one of my websites just disappears out of my "List of Account" tab. Any ideas of what I can do to prevent this from happening again?
Your hosting provider will need to help you with this. As a reseller, you will not have the access needed to properly diagnose and fix this. If your hosting provider is not able to find the cause of the problem, ask them to submit a ticket to us on your behalf.
There is nothing that you would be able to install as a reseller, since you are not the server's administrator. You need to talk to your hosting provider about this.