Sorry for replying to the old thread but this one comes up as the first link when you google "Moodle LTI URL Disappears". So to help out anyone with this issue the solution is indeed simple. As John points out, it is in the tool provider configuration, but it doesn't have anything to do with the provider themselves.
The solution is to go to Site Administration > Plugins > External Tools > Manage Tools and edit the configuration of the tool. Under "Tool configuration usage" set the drop down to, "Do not show; use only when a matching tool URL is entered."
First, a nod to the use of a semicolon.
That setting prevents the preconfigured URL from disappearing when you edit a link.