Protected Li-ion batteries charging / discharging in parallel?
As always, it depends. How closely matched are the capacities and internal resistance of the batteries in parallel and how much current will you push? If very little compared to capacity then most likely no problem. A lot of current and big mismatch in capacity and internal resistance then the following will happen:

(Image stolen from Wolf at secondlifestorage.com, but I'm sure he won't mind)


Link to thread: https://secondlifestorage.com/showthread.php?tid=7873


  I know that PCM will disconnect each battery randomly during charge and discharge


Sounds like the BMS (you call them PCM?) is protecting the cells from this very event. If you lower the current, does this stop?


  Am I missing something?


How does the charger/overall system react to the BMS/PCM tripping in rapid succession?