New emulator in AVD manager gives "no longer exists as a device"

This problem occurs when the AVD manager is looking for a hardware profile and can't find it, even though it exists. I have a feeling that this is caused by a bug in the latest tools that cause hardware profiles to be saved without a proper id, because profiles made a while ago are still working correctly (until you edit them). The following fixed it for me:

In your user profile folder, find devices.xml inside the ~/.android folder, so on Windows you'd look for C:\Users\Me\.android\devices.xml.

Open the file and look for a device with the name that shows in the error message, in your case 'Android Wear Round'. It'll look like this:

    <d:device>
        <d:name>Android Wear Round</d:name>
        ...

Duplicate the line with the name and change the tag to d:id, but keep the name, like so:

    <d:device>
        <d:name>Android Wear Round</d:name>
        <d:id>Android Wear Round</d:id>
        ...

Return to the AVD manager and hit refresh; the virtual device should be repaired now.