I have already so many problems because of cables, normally it's either the cable itself or the connector. Probably the cable just over-qualified or just broken. Have you tried to exchange cable port into unusable one in the switch?
What I did is reinstall the driver and uncheck all in power management in device manager under your ethernet card.
Quick update: At the moment it works at 1Gbps. I'm still monitoring this issue. I hope it remains working as usual.
I had a similar problem.... turn out it was the cable that was bad... It tested ok for continuety, but it seems the crossover noice was to high for 1Ghz spec....so the controller downgraded the speed like you describe... Just get another cable(less fancy, blingless) of a normal type Dont by ethernet cables by looks or on ebay/aliexpress.... they are in most cases just junk...