Refresh Token Invalid

We recently updated our Application and I am getting an odd situation. I had to re-authorize and generate a new Access Token and Refresh Token. I then stored the tokens and started using the new Access Token, and that works fine.

However, when the Access Token expires and I try to refresh, I get this message:

{"error":"invalid_grant","error_description":"The refresh token is invalid or expired."}

I've looked through other questions and the common suggestion seems to be that another Refresh call may have happened that overrode the Refresh Token I stored.  I don't think this is happening, but I suppose it may be possible somehow. My question to help confirm this is, when the Refresh Token request happens, does it invalidate both the Access Token and the Refresh Token? Because the Access Token I got continues to work for its expected 24 hour lifespan. 

Second question - does the "Long Lived Refresh Tokens" feature in the Application settings work? I don't see it mentioned in the documentation, but saw it when I was looking at our Application. But if it does, I would use that option instead.