Hi,
To Login just an iMessages account in Messages on the Mac there are two connections to the servers.
One is logging in and the other is to "See" who is on Line.
Whilst not quiet the same as an AIM or Jabber Buddy list the process is effectively the same as seeing Buddies ON line separate from your login process.
There can be situations where you get a partial Login means you cannot verify the people on line whilst appearing to be logged in.
There is no indicator whether you are or not (Unlike a Buddy List account where they all go Off line and it can say Disconnected).
I would try the Sign Out button in the iMessages account on the Mac.
I would then Quit the app and then Restart it before turning the account back On.
There are ways to remove the Apple ID and Login details and making the app start afresh if we need to go that far.
For iMessages that have been missed in between time it is likely to be a mixed picture on retrieving them based on the time taken from them being sent and the servers "thinking" you are logged in and send you them.
You may only get those sent after you reset the login.
9:53 pm Sunday; October 30, 2016
iMac 2.5Ghz i5 2011 (Sierra)
G4/1GhzDual MDD (Leopard 10.5.8)
MacBookPro 2Gb (Snow Leopard 10.6.8)
Mac OS X (10.6.8),
iPhone 6 iOS 10.x and an iPad (2)