Welcome to the site Noobiq :ciao:
What type of connection do you have? Cable, DSL, or Dialup
Next question is if you are wireless(WiFi connection to Modem)
We need to know how you are connected before we can tell you how to stay connected
Can you check the network card properties in device manager, click on "power management" and uncheck the "allow the computer to turn off this device to save power". I've seen that cause problems like this before, so it's worth a try.
Should there also be an option to reconnect when disconnected?
My wireless reconnects after waking up