This typically points to a network issue or possible bad ethernet port on the Digi hardware. What happens if you run a continuous ping to the Digi device from the RealPort host in comparison with other nodes on the network (i.e. is it only the connection to the Digi device that is dropping or the overall network)?
What Ethernet LED activity is seen on the Digi unit when the disconnect occurs? A lack of a Link LED can point to possible hardware issues with the Ethernet port, cable or switch/HUB.