I can confirm the issue is now resolved! After switching to an optical connection (from analog) using the device I linked above, I now no longer have any drop outs. It seems the device forces the streamer to maintain a persistent connection, even when there’s no audio on the line.
Huge thanks to @Gramps for the idea.
Just to recap, the device I am using is a Behringer UCA202 which connects to my Macbook Pro via USB. The TV Connector is then connected via the optical output on the Behringer. Works like a dream.