We have a reverse osmosis system on our kitchen sink. The small 'faucet' that dispenses the filetered water is leaking out of its breathing tube. I disconnected it assuming it was blocked but can't find any evidence that's the case. Any suggestions would be appreciated

What brand system do you have? Could you further explain what you call a breathing tube?

You have probably already fixed this problem, sorry I wasn't here in February to help you out.

If you remove the Faucet (the neck part) from the base (where the on/off valve is) you should see two orings. Make sure that those are not corroded or have anything on them.
Your problem is that those orings are not sealing and water is flowing in that valve and is allowing it to go out the "breathing tube"
If those o-rings are intact and no water is present then you will need to get a new faucet because something has become warped or tweaked and will not create that seal.
Let me know if you need further assistance