Well, I will assume this is not related to any internet connection, just your network adapter and the router. Since it seems to be dropping the connection for some reason, please post the results of an ipconfig /all command when run in a command prompt window. You can copy and paste or use the snipping tool to take a picture and attach using the paperclip on the advanced reply window. Edit as you see fit.
You can also check the Device Manager and check if your network adapter is set to allow the system to turn it off to save power. Mine is set that way, but you might uncheck that to see if it makes a difference.
The next time is loses its connection, open the adapters panel (ncpa.cpl) and disable, then re-enable the adapter. It should resync and regain your connection.
I understand this is a wired connection, but I will assume network connections are dropped during a sleep cycle.
If you need any specific information, don't hesitate to post back.