Ethernet connection to Mesa 7i76e disconnecting on its own after one minute

sudo apt install ethtool
-
And the network is not set up properly or not connected???

Yes, the network is not setup properly (no fixed IP address)
 

I did a video recently about this

I installed ethtool and I am still getting command not found 

probably needs sudo ethtool

sudo ethtool works 

type: sudo ethtool --set-eee eno1 eee off

this will be lost on boot so to make it permanent
type
sudo grub-customizer
open the second tab and on the line it says quiet, add: igb.EEE=0
save and reboot. 
check eee is off again with ethtool

With energy efficient Ethernet enabled, sometimes your NIC has a holiday which is not good for latency

Also type man hm2_eth and follow the instructions so disable coalescing if you have not done that yet on your 10.10.10.1 NIC

once all that's done, do the ping command PCW asked for and share it. It should be pretty good now.

The reason ethtool is not found is that it's installed in /usr/sbin/
and that's not on the default user path. (but is in the default root path)

The sudo grub-customizer did not disable eee for me.