Kernel.org: 5.1.5
sid (unstable): 4.19.37-3
buster (testing): 4.19.37-3
stretch (stable): 4.9.168-1+deb9u2
jessie (oldstable): 3.16.64-2

Debian GNU/Linux device driver check & report

Giga-byte: Gigabyte GA-965P-DS3

PCI IDWorks?VendorDeviceDriverKernel
11ab4364YesMarvell Technology Group Ltd.88E8056 PCI-E Gigabit Ethernet Controllersky2v2.6.25-

Works fine at 100baseT, will only transfer data for a few seconds at 1000baseT before the transfer freezes, the machine drops off the network and the following shows up in /var/log/messages:
kernel: sky2 0000:04:00.0: error interrupt status=0x1
kernel: sky2 eth0: descriptor error q=0x280 get=254 [a100004200000000] put=256
Tried with kernels 2.6.21 through 2.6.24 with same results.