Have tried different cables and chargers. Checked that the Soundcore Boost is drawing >1.5Amps during charging. Tried charging it whilst speaker turned on and off. Same problem. It appears to charge up fine with all four indicator lights coming on after a few hours and current draw will drop to a trickle. As soon as I unplug it and switch the speaker on, the four indicator lights drop instantly to three.
Such battery behaviour (charged to 100% on mains; big sag on unplugging) is generally seen with a worn out lithium rechargeable. I can only guess that my unit has a bad battery. Looking at Amazon reviews, someone else has also posted a similar experience with his unit.
I guess it's time to contact Anker support for a return and replacement.