SQL Server - "The connection must be in an opened state."
This is a very interesting error. Please note there is no error code of any kind associated with it. This means it has to do with SSMS rather than SQL Server.

And this specific error is telling you that the SSMS no longer has active connection to the server. It is possible that this might be the case of faulty switch or similar, but I doubt it.

My recommendation is to check settings pertaining to power saving options of the computer you use in general or your NIC in particular.

In other words - Windows powers off you network adapter while on idle to save power. Might want to check adaper settings as well - my had all sorts of options like "EEE" or "Green Gigabit" enabled...

Addendum

Having similar issues lately when working via wireless connection we - my IT department and I - tracked the issue down to wireless adapter on my laptop and speculated that reason might be some undocumented or inaccessible setting linked to power consumption. It improved only after relentlessly updating drivers to latest possible version using both Intel and Dell updating tools. 

Until then same symptoms: connection says it's live, but running queries randomly generated above error. Windows says connection is live, SSMS concurs, no - literally: zero - entries in Windows logs even remotely touching on networking. All is well when using wired LAN.