I've experienced this in Unity Connection 10.5 & 9.1, but it may affect other versions as the Media Master applet is notoriously flakey.
Attempting to save an uploaded recording in the Media Master applet results in an error "Failed to record name", the workaround is to select "use phone" for playback (see screenshot below), upload the recording, play it & then saving works; not playing the recording or playing it through the computer fails.
For those of you having difficulty even launching the Media Master applet, edit the Java Runtime Environment (JRE) settings via Java in Control Panel (for Windows users). Add the IP address & FQDN of the Unity Connection server to the Exception Site List:
If you're using self-signed certificates, recent versions of the JRE don't like this so either import the certificate via Manage Certificates or generate a certificate from a trusted CA. As a general rule it's better to have certificates issued by a trusted CA, but this may not be feasible in all situations.