We do not have an Errata sheet for the AXP803, do we? Maybe it has to d!)o something with the undervoltage lockout settings in the dts..., but that would be silly, or a bug...
As far as I understand the datasheet, there is only two states for the charger to be in if it is enabled, and that is more or less hardwired. Under 3.0V it charges slowly with 1/10 of the programmed normal current (which doesn't seem to happen either) and above 3.0V it should charge with the programmed online/offline charge current... maybe there are some fault conditions that get triggered that turn it off... but I haven't found anything in the datasheet yet to explain the behavior and didn't manage to trigger it myself yet...
As for recovery I would try to manually charge the LiPo a bit with a bench lab supply, set some save end voltage like 4.0V and current limit to 2A and just hold some test probe to the terminals (disconnect from PCB first!) for a couple minutes, that should get it back up enough if it is an undervoltage problem