Our server has a warning: "This server is using illegally downloaded software"

It probably means that you're using a protected leak like "Admin popups" when you restart the server it will say something about you server using leaks and it will not start up.
I'd say get a local host or a dev server and slowly put all your leaks onto the server until it starts happening again.
If you're not using leaks then I don't really know what to tell you :/