Unfortunately, no such thing is possible, it is a live server.
Only thing I noticed is that server has three network interfaces. I do select one in remote utilities but could it be this is confusing host software and is trying to switch between interfaces which is causing issues then?
If you are using your ID server as you mentioned, the IP address of the Host computer has nothing to do with remote connection. You are connecting to your Host through your ID server, which acts as an intermediary.
Have been having the same issue for the last few months on my laptop. However, I've noticed that connections with the IOS and Android apps are stable and do not suffer the same online/offline problems. Certainly not to the same extent as the PC.
Could you please try the latest beta and see if the issue persists. You can download it from here https://www.remoteutilities.com/download/beta.php . Note that if you upgrade you should upgrade both modules, Viewer and Host, for proper testing results.
We need to isolate the issue first. For example, we could set up a Host on our testing machine , point it to your ID server and leave it working for a while as well as give you access to that Host. You could see then if the connection is stable or not.