Yeah, this is what I primarily did when I wanted to save some audio from imessage. It'd end up in voice memos nicely organized. It no longer works that way.
I did find a way to at least email myself the files. You can go to "info" under the imessage conversatoin and select "attachments" after which you can individually go through all the audio files and share them. (email in my case.) Of course, you would have had to have the audio message expiration time of 2 minutes disabled under options.