I'd start by inspecting the gateway logs on both the primary and backup gateways to see what errors or warnings, if any, are occurring around the time of client disconnects. I would also inspect the vision client logs via the diagnostics menu, again, looking at around the time the client disconnects to see if there are any warnings/errors.
Hopefully there is something in the logs that can point you to a more concrete cause.
Have you been able to narrow down to a specific screen or two on the project, or does it seem to occur regardless of what screen is active?