Hi and welcome to the Bome community!
Well there are many points of possible issues so I think I would need to understand the exact paths that you have established between each point.
The first point is to determine whether Bome Network Pro is showing constant connections between the systems. If it is then it will rule out quite a bit of a Bome Network Pro issue.
You say you have 2 PCs and to Macs. Is one pair a redundant system of the other for failover or are they both running in parallel for separate purposes?
It is probably important when there is a failure to determine the point of failure. I understand that this may not be possible in the middle of a service so it would be helpful to see if you can get the failure to occur at a safe time to troubleshoot.
Fortunately Bome Network Pro has a logging window that you can open and view MIDI messages. There is a green bar on the bottom of Bome Network Pro windows when you float your cursor there. You can drag up this bar and enable verbose logging to see what is happening. See the link to an illustration below.
https://i.imgur.com/JALc33a.gif
What I suggest is you open this window on the sending system(s) first to see if you have proper MIDI activity. If you do, then do the same on the receiving system. If there is activity on both sending and receiving then that rules Bome Network out (mostly).
Then you can focus on viewing what is coming into and going out of Pro-Presenter to see if it is working correctly.
There are several tools to view these ports and you can even do that with the free trial version of Bome MIDI Translator Pro (Scroll down on the page to get to the download link) .
I have found the most common point of error is on the Windows side as two applications cannot open the same MIDI port at the same time. It is important that only one application has a given MIDI port open as the first application to open that port will stop any other applications from using it.
For further troubleshooting, you start with the point of origin and monitor activity at points through the full MIDI path until you see where it stops.
Not knowing the specifics of how the ports are configured on each application, I cannot provide much more assistance unless I know. A quick diagram might help with perhaps screenshot of how MIDI is configured at every point in the path.
If Bome Network Pro itself is dropping and reconnecting then log entries I mentioned earlier should help.
This post, will show you where the log files are stored on each platform if you need to share them.
Steve Caldwell
Bome Customer Care
Also available for paid consulting services: bome@sniz.biz