I have Linux Mint 18, and always (with Linux Mint 17 too) have a problem with the connection to some repositories in the update option. The solution that I found is to run this in terminal and it works fine:
sudo echo "nameserver 22.214.171.124" | sudo tee /etc/resolv.conf > /dev/null
But, I have to do this every time when I reboot or shutdown my PC.
I tried a lot of options from the internet to run this command on startup, but they don't work for me.