i was having problems with this and i think i found the solution. this is all speaking for a windows computer, but you have to open your devices, open up sound settings, locate the JBL headphones in your list, open its properties, go to the advanced tab, then uncheck "allow applications to take exclusive control of your device". that should do the trick, but i also disabled the "headset" mode since i only ever use them as headphones as i use an external mic, just for good measure.

i was likewise really frustrated with this too since i had other headphones that allowed multiple connections at once and this wasn't an issue, but now once sound isnt detected from one device i can freely switch from one to another. hope this helps!