Ethernet connection turns off when my Mac idles
I had similar problem with the wifi I use.

It would disconnect me after certain time of inactivity.

So when downloading big stuff it would disconnect me, unless I was active on the computer/web.

To prevent wifi been disconnected during long downloads or me not interacting with it:

In Terminal I entered following:

ping -i600 google.com


That would send a ping to Google than wait 600 seconds to send another ping and on and on...till I hit the control-C to stop it.

That will tell wifi I am active so it will stay up all the time.

The 600 sec (10 minutes) is a choice, and it worked for me.
In my case it was the WiFi service provider that cut me off after been inactive for a while.