There is a battery draining issue even when the A6000 is turned off. The problem is caused because of the viewfinder proximity sensor seems to stay turned on even when the camera is turned off. The solution is to disable viewfinder and let just the screen (monitor) on. Enable airplane mode helps also. This solution was described by kentender at Sony Community Forum and by The Photo/Video Show channel at Youtube.

I have found even with the viewfinder switched off ( I don't use it at all) and the camera in airplane mode, the battery still drains at an incredible rate, why I am not sure. I now take the battery out when not using it for long periods.

no problem with my A6000 in airplane mode, whatever viewing mode is on.

 

however big problems with my A7, same settings, it drains a battery in 2 weeks. both have been updated.

IIRC the "computer memory" battery in these

is not a disposable coin-sized lithium, but is a

rechargeable, charged by the main operating

battery. So [again IIRC] leaving a camera too

long without any battery could return all your

personal settings to defaults, lose the date

and time, etc.

 

It doesn't matter how long a camera sits with

no battery waiting to be initially sold, cuz no

personal settings or date/time etc need to be

preserved on a brand new camera.

 

`

For those who still facing this issue there is another solution. Update smart remote control app. It is necessary to uninstall the app and install again. After that I had no battery drain even with viewfinder enabled and airplane mode turned off.