Hi Supertrouper

First the basics
Try reinstalling the drivers/update drivers.
Check your protocols (TCP/IP, IPv6, Network monitor driver, Client for microsoft networks, QoS packet sheduler, file and print sharing)
Check your windows error log file to see if it found any problems at the time that the device disconnected.
On the host machine ping 127.0.0.1 when you are getting no signal and if it comes back timed out or with an average time greater than 0ms then you have a hardware problem.

Other options
Try moving the card to a different PCI slot and check that your computer automaticaly allocates IRQ numbers to the devices.

Like Dellae said it sounds like a hardware problem.

Hope this helps