Same happened with me. AUX low volume cuts out and bluetooth is OK. I called JBL, They referred me to a JBL repair place by me which I spent a day to sort out, and they told me this:
If bluetooth: The signal is strong and reliable.
If AUX: the signal or volume from the output (computer/phone etc) must be high (over 80%) and you physically reduce the volume on the JBL and it will work just fine. It has been over a month for me and this is the legit fix!
I told the guy, this is broken though... Why would a reputable company like JBL do this, he obv didn't know but yea, basically JBL created an incredible speaker with a f***ing annoying glitch. I only use AUX at home and also for portable DJing out and about. Outside is OK as the volume is high anyway but this !#^&@! me off at home as the bass will !#^& off my neighbours and why should I WALK to my BLUETOOTH speaker every 2 minutes to MANUALLY turn the vol up/down? Big fail JBL... big fail.