Hi Galileo1564,
The problem appears to be fixed in the new Window 10 V 1903 build 18362.116 just released to general users on 5/21/2019.
I upgraded all my PC's from v 1809 build 17763.529 to v 1903 build 18362.116 and the PC's that were previously failing with 1809 are now working fine with the workaround disabled in Task Scheduler.
All my PC's are showing up in the network and keep showing up normally after PC restart.
Unfortunately the bug is still present with Windows 10 preview 20H1 build 18898.1000.
Since it appears to be fixed with 1903 I hope they add the same fix in the next 20H1 insider preview.
As you can see, I have not checked my Outlook Email account in a very long time. I am not supporting the church network that was having that problem. But I am now supporting a different church P2P network and they are still having the same problem. I will look at the suggested problem bandaid on the new network. The workaround for the employee users is to type in the search box the computer they are trying to access. Doing that it immedily brings up the compter on the network. I then showed the user how to right click and pin the network computer they are try to access to QUICK ACCESS. This bandaid is a quick fix for the problem. So the problem has not been fixed even up to the latest 1909 verson. But thank you for responding and giving me another workaround.