I had considered setting up my own Remote Utilities relay host to see if that would help, but have just been too busy. The problem exists between each location I connect to and is limited to Remote Utilities and not connections. My office is on a Fiber network which has only gone down 2-3 times within the last 4 years. I still use Remote Utilities and like it, but this problem is not a networking issue, or at least it isn't an issue that isn't solvable by better try/catch blocks within Remote Utilities.
Large file transfers were possible without interruption, but the Remote Utilities connection was unstable for more than a few minutes at a time (5-20).
While using, my connection was never reset and operated smoothly for hours at a time. Because of this, I used Remote Utilities to connect to the computer, get the ID and password and connect using where I could see the menus. I was connecting remotely to a client's computer using Visual Studio and the right click wasn't bringing up the menus, or more specifically context menus were not visible during the remote connection. For us updating the ID was easy, but it didn't solve the problem.