I know a little bit about Windows drivers and I have a couple ideas as to what may be causing these issues, but unfortunately they might not solve this problem.
I don't have a USB->Ethernet hook up yet in my IO (been checking local sources, and have seen the DLink and Netgear varieties, but not the SMC one--which is best BTW?) so I'm not totally sure what the drivers for these look like, but I'll venture a guess and say it's either the drivers (the WDM USB or Network ones--could be either) or it has something to do with the power consumption of the USB device. If it's the power consumption of the device, then I don't think there is anything that can be done. However, if it is a software/driver issue, a couple things could be checked (these suggestions apply to those running any flavor of Win2K):
Next time you lose network connectivity, check the Device Manager for anything that has an ! next to it. There might be something under "Universal Serial Bus Controllers" or "Network Adapters" (this is what I'm not sure about--which of these, if any, the USB->Ethernet adapter will show up under).
If indeed an ! shows up under either place, it may be possible to restart ("Enable") the device without having to do a hard reboot. Do this by right clicking on it and choosing "Enable Device" (I think--something like that).
Another thing to check and see is if the service is what has stopped for some unknown reason.
To check and see (and restart the service--not the system), go Start|Run and type in "services.msc" to find out (don't forget the ".msc", otherwise you won't load the GUI for it, just the background services host. You'll need to be logged in as a user with Admin privileges. Look specifically for any services marked "Stop" under the "Status" column. If you see any that appear to be network related e.g., DCHP Client, DNS Client, Internet Connection Sharing, IPSEC, Network Connections, TCP/IP NetBIOS Helper and Workstation, you can right click on that service and choose properties to Start/Stop/Pause/Resume this service.
If it is a software/driver related issue, these suggestions might help track down some more info needed to diagnose this problem. If nothing seems out of the ordinary here, then I'd conclude it had something to do with the USB power draw. Something that most likely can't be fixed from software.
If the software/driver/services avenue works, I'd conclude that the driver is leaking memory or some other such Bad Thing.
If it is something like the power draw, and you haven't soldered you USB->Ethernet to the second set of USB pads (I think I read a thread saying this can be done--yes/no?), you might try plugging a *powered* USB hub into the IO and then the adapter off that to find out.
Hope that helps a little