I can't find the types that you named, but they are Intel Pro/1000 GT cards (new ones). This is the link to this product:
http://www.intel.com/network/connectivity/products/pro1000gt_desktop_adapter.htmSince the internet connection is always stable when I bypass the M0n0wall, I can't imagine there's a problem with cables and the switchbox.
When I read your comment, the most likely possibility is that the mainboard with VIA 694 is the 'bad link'; this chipset isn't as stable as, let's say, an Intel mainboard. Since the M0n0wall is more stable with the Intel cards, but not perfect yet, this could very well be a reason.
Can I adjust the timeout-time somehow? When this doesn't help, I think I'll try another PC (I've got several).