I would suggest it is highly unlikely to be a static build up, the static voltages required to physically break a connection in a patch cord (as you stated by the continuity tests), would be massive and leave some fairly serious tell tale signs!
Is it the same ports on the patch panel causing trouble?
or is it the same port(s) in the switch causing trouble?
I have seen many instances where admins try and keep patch cables nice and tidy by routing patch cords through cable management systems and inevitably end up putting such tight bends and kinks in the cord you can see the stress marks in the outer sheath! Afterall why use a .5m patch cable when you've got a 10m one lying around?
EMI can/will cause links to drop and magically reappear, any new electrical cables/appliances been put in place recently (by appliances, i'm not talking toasters, more like 3 phase equipment, microwaves etc.)
Do not rule out the switch either, next time it happens, unplug from the port on the switch and plug it in to a different port on the switch, see if a link appears, could also be the NIC, had one like that today actually, link went dead on the switch but the activity light on the NIC was going mental, unpluged, swore like a sailor, plugged it back in for giggles and away it went, failed 2 hours later, replaced the NIC and had no more problems!
Does the problem happen at a particular time of day?
Lot's of questions, but that's how you get lots of answers!