Hi,
If you were Saving on Close then you may have been storing the Conversation on a session/day by day basis whilst dismissing it from view in earlier version of Messages.
It seems that the x that appeared when mousing over a chat in the Side bar on a Mac version allowed you to dismiss from view the Chat whilst storing it as a Saved Chat.
Saved Chat also get summarised in the chat.db data bases in ~/Library/Messages and enables better recall of the "history" of some chats.
The reason I say "Seems" is since Sierra it appears that the x deletes the chat removing it from the Saved Chats file but like you I have experienced partial "recoveries" of past conversations without being able to pin down which bits still work and which bits don't.
I tend to delete on my iPhone and iPad as I used to know that it was Stored on my Mac.
This does not seem to be an option now and I have things showing on the Mac version's Side Bar that previously I would have dismissed.
As I came from iChat and AIM chats I don't have that many spare iMessages conversations to try and experiment with.
Therefore a Search may show items that are in the Archive Folder for Saved Chats but searching back up a conversation will be pulled from the summaries of the items that are in the chat.db items
The archive folder is in ~/Library/Containers/com.apple.iChat/Data/Library/Messages/Archive
On some people's systems this last item may be an Alias point to an Archive Folder in ~/Library/Messages (along with the Attachments folder)
9:07 pm Monday; December 11, 2017
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 11.x and an iPad (2)