Ok progress.

This is related to the Button LED hack. With the LEDs turned off, the only missed interrupts are a few that occur during the portion of the boot cycle that they are lit. As soon as the LEDs are turned on interrupts start going missing. I'm running some more tests to try and work out whether the quantity that go missing is related to the illumination level or not. First indication is that it is not.

Now as far as I can see there is one very obvious interaction that could be at play here. The PWM current flow through the LED circuitry could be at a frequency that interferes with the IR reception.
Another possibility is that the oscillating current drawn by the knob button is causing a fluctuation in the IR receiver's supply voltage and that the IR supply isn't dealing well with it.

Now this doesn't happen on my player that also has button LEDs, so I'm still wondering what the difference is.