Hi,
Does not sound like anything I have come across.
Messages can have several Accounts several of which can also do group chats.
The AIM accounts can as can Jabber Accounts that would also include a Google ID if you were using one.
Bonjour cannot do group chats.
Of course the iMessages account can also do Group chats.
There was a Thread I posted to recently that had no text/chat saved after the session finished. (not for any chat, so similar but different).
It turned out this was iMessages but the person had transferred the Chat.db items in ~/Library/Messages from another computer and his Mac User account on the current computer did not Own the files so he could not Write to them to store the info.
Messages can store Chats in two places.
Open a Finder Window an use the Go Menu whilst Holding down the ALT key.
Select the Library that now appears in the Menu.
Navigate to Messages.
There are three chat.db item here and you have to Own the file and have Read and Write Permissions.
"Save On Close" saves the chats to:-
~/Library/Containers/com.apple.iChat/Data/Library/Messages/Archive
This is full of dated folders that have the chats in them - if a chat continues over several days/weeks then each part for that day (or Session if you closed Messages) will be in a separate folder. IT is the app that puts them "back together" if you dismiss (but not delete) the chat from the main window but then restart it (shows "history").
TO check you Own a file do a Get Info on it.
So for the chat.db item navigate to the folder and highlight one of the File and then use the key combo of CMD + i (Get Info if you Right Click).
This opens the Info panel.
Scroll to the bottom.
In the Permissions section you should see your shortname listed.
It should also say you have Read and Write Permissions.
Highlight this line.
Now Unlock the Padlock
Next click on the cogwheel like Icon under the list.
This should say "make yourshortname (me) the Owner" but it should be greyed out as if already done.

Of course you need the Read and Write Permissions to the folder to get you to that point - as in ~/Library and the Messages folder.
For the Saved Chats - the Archive folder this is a lot more folders and the fact a chat could be saved over many days or even weeks you may have to check many files and folders.
iMessages chats can be broken down in some sessions/days as well.

Note the Path Bar across the bottom on this picture.
As a Start I would check the Saved Chat appear to be correctly Saved.
The Chat.db items can be opened in TextEdit (Open With) but you will find that they are not that user friendly but with patience you should be able to see the chat entries.
As I said It can be difficult and it is easy to miss a specific line of chat.
I would set the ~/Library/Messages folder to CoverFlow view and then show the Modified column (Finder > View Menu > Show View Options
This should show whether the file are being updated (Written to).

This will at least get you to a point where you might be able to tell where the issue is.

9:08 pm Thursday; September 1, 2016
iMac 2.5Ghz i5 2011 (El Capitan)
G4/1GhzDual MDD (Leopard 10.5.8)
MacBookPro 2Gb (Snow Leopard 10.6.8)
Mac OS X (10.6.8),
iPhone and an iPad (2)