TestComplete is running on the same machine as TestedApp, so how can it be a firewall thing or related to networking? This has to do with the TestedApp closing, and then re-opening, and loosing all the object mappings.
I am not sure about the details of your application, but it could be trying to communicate with something else, these errors can also happen due to something local as well.
You said that you were seeing the RPC error which is a Windows error not a Test Complete error which is why I pointed you in that direction.
Losing the object mappings is something different entirely, we would need a lot more info for that, specifically screenshots of your mapping properties and screenshots of the object browser and properties for the object you can't find.
