It seems quite clear that the speaker (JBL Xtreme 2) contains a digital ‘gate’ which silences all audio below a certain loudness level. In my case, I’m sending the audio signal to the speaker from a DAC with a line level output (this is a weaker signal than you get from a headphone output). I could not prevent the speaker from ‘gating’ (cutting off) the sound, so I inserted a small battery-powered headphone amplifer between the DAC and the speaker to boost the signal strength. This solved the issue. An alternative solution is to connect the speaker to the headphone output (of a TV, for example), as this should give a stronger signal.
This ‘gate’ (which is probably implemented in the software/firmware) should be removed by JBL as it achieves nothing but causes a lot of problems when using the analog audio input.
As others have stated above, if you still have problems when using a headphone output, turn the device (TV etc) to maximum volume and reduce the volume on the JBL speaker to whatever level you desire.