I'm giving a try to Debian (7.8 x64) and I come across a problem concerning network connection.
I boot up the system using either dhcp / static IP and after some minutes (or maybe just a small amount of idle) the network does not work anymore (no ping on any host in my network, no INTERNET connection, nothing).
Running ifconfig shows the eth0 as being up, running ifconfig eth0 down/up doesn't help, neither service networking stop/start.

Rebooting the computer makes the network work again.. only for a few minutes and then looses again
The same issue happens on Kali Linux live using default network configuration (as dhcp) or using a static IP.

My primary OS is Slackware 13.37 and I don't have that issue there. I'm new to Debian world and I try to fix it up.
What could make the eth0 to loose connection suddenly or after a small amount of inactivity? Maybe is some powersaving involved?

It's difficult to know, but I would start by checking the last 20 or 50 lines of the dmesg output as well as /var/log/syslog, /var/log/messages and /var/log/kern.log when the problem happens, to see if there are some clues there.