I pretty much have mine connected full time without issues. As Bit mentioned the real issue is the networking card (more specifically Wi-Fi if connected to a router), but when I rebuilt this machine in July I found the biggest culprit is a wi-fi router doing an "auto-detect" of new devices. That can be disabled, is totally unnecessary, and sends a query pulse every 4 seconds that is a "high priority" process. My machine is hardwired to the router, but that query is atrocious. I also have anything "auto" disabled on this machine (or set to manual start) - type in "Services" in Windows search and can do this there, but be advised some things (especially Adobe) will reset status to "Automatic" the first time you manually run them. Between "Services" and "msconfig" you can catch 99% of things you don't want running on there own, and an internet connection does give some of these reason to "go active" on you. Easiest fix is to disconnect when using the DAW if desired.
As long as you judiciously use the internet, there is no need to get overzealous with things, but disconnecting when tracking can be useful to remove that batch of resources.