FWIW, I to have this issue, I don't want to hijack these thread but I thought it pertinent to outline issues here too. I wanted to search for "Intel(R) Ethernet Connection I219-V" and this was the second on the list
However, my setup is somewhat different:
Laptop - HP EliteBook 1040 G3
BIOS update (01.08) - latest
Windows 10 64 bit, build 14955
Tried Driver version 12.13.17.7 (13/08/2015) and the latest Version 21.1 (September 28, 2016),
With the same issue. When the laptop is completely shutdown power off), then started from cold, the Ethernet NIC will detect a link of 1Gbs immediately and connect with no issue.
As son as the laptop is put to sleep, then woken up, the NIC will only say the link is 10Mbps, but not actually connect properly and pickup and IP address.
I have tried to disconnect the Ethernet cable, disable/re-enable the adaptor, it hasn't resolved the issue. Only a full shut down will cure the problem. .
Any further thoughts beyond what you have said above.