When I turn on my P3A remote, the four white LEDs come on but the left hand LED blinks red and the controller beeps all the time, every half second - which I believe indicates critically low battery.
I plug in the charger and the white led's cycle up and down as though charging and then after a while they go out - battery charged?

However when I turn the controller on again I get the same problem, all four white LEDs on but the left hand one flashing red and the controller beeping.

Any suggestions please? Looks like a defective battery?

Hello there cheddar-man. I am sorry for the trouble this has caused and thank you for reaching out. Kindly please post a short sample video showing the said issue for us to see and assist you further? Thank you.

I have resolved this issue.
It turns out to be a stick/camera calibration error on my behalf. I calibrated the sticks but didn't also do the camera!
I have opened up the RC to check the battery and it was showing 8.33volts, so fully charged.
On another forum someone mentioned stick calibration so I re calibrated the sticks AND the camera and everything works just fine.

Lesson learnt!!