First check if Logitech has updated drivers available and try them. If it still happens:
Check if you have USB Selective Suspend enabled in your power plan settings.
Control Panel > Hardware and Sound > Power Options > Click Change plan settings for your current plan, then Change advanced power settings. Look for USB Settings > USB Selective Suspend. Disable it.
There's discussions about your headset on the Logitech forums. People have reported their disconnecting headset issue was due to interference from wireless telephones or routers. If you have a wireless router and the above do not work you can try changing the channel your wireless router uses. Others reported getting theirs replaced by Logitech and the new ones working fine.