I had to check what more could be the explanation to this strange behavior and found out that there have been a couple of changes made to the INF files besides the signing, changes which Microsoft recommends to make sure the USB COM port driver they provide is installed and found on every type of Windows. (As I said, we do not deliver a "driver" since the driver in question belongs to Windows itself, we only provide a file which tells Windows that we want it to use its driver with the RRC).
If now in fact those changes instead have made the system unstable and not working as good as before then it is truly nuts! We will certainly have to look into this!
Thank you for your help and patience!