Hi vhgroup - I see you have a NUC6 (not sure on the model) - though has a different Ethernet Chip - but we have the same driver. Mine doesn’t experience th3 same issue that you have described.
Dumb question…. Did you have wireless enabled at the same time as Ethernet?
nuc6:~ # dmesg | grep -e DMI: -e e1000
[ 0.000000] DMI: /NUC6i5SYB, BIOS SYSKLi35.86A.0073.2020.0909.1625 09/09/2020
[ 1.263095] e1000: Intel(R) PRO/1000 Network Driver
[ 1.263096] e1000: Copyright (c) 1999-2006 Intel Corporation.
[ 1.263108] e1000e: Intel(R) PRO/1000 Network Driver
[ 1.263109] e1000e: Copyright(c) 1999 - 2015 Intel Corporation.
[ 1.263306] e1000e 0000:00:1f.6: Interrupt Throttling Rate (ints/sec) set to dynamic conservative mode
[ 1.464787] e1000e 0000:00:1f.6 0000:00:1f.6 (uninitialized): registered PHC clock
[ 1.532147] e1000e 0000:00:1f.6 eth0: (PCI Express:2.5GT/s:Width x1)
[ 1.532153] e1000e 0000:00:1f.6 eth0: Intel(R) PRO/1000 Network Connection
[ 1.532223] e1000e 0000:00:1f.6 eth0: MAC: 12, PHY: 12, PBA No: FFFFFF-0FF
[ 26.570861] e1000e 0000:00:1f.6 eth0: NIC Link is Up 1000 Mbps Full Duplex, Flow Control: None
nuc6:~ # lspci -v -s 00:1f.6
00:1f.6 Ethernet controller: Intel Corporation Ethernet Connection I219-V (rev 21)
DeviceName: LAN
Subsystem: Intel Corporation Ethernet Connection I219-V
Flags: bus master, fast devsel, latency 0, IRQ 125
Memory at df100000 (32-bit, non-prefetchable) [size=128K]
Capabilities: [c8] Power Management version 3
Capabilities: [d0] MSI: Enable+ Count=1/1 Maskable- 64bit+
Capabilities: [e0] PCI Advanced Features
Kernel driver in use: e1000e