Solar panel does not charge after lipo battery is low
The documentation states that until the battery voltage reaches 3V, it will only perform trickle charging of the battery (very slow charging), at a maximum of 90 mA. This is to protect the battery:

Trickle charge: Since the internal resistance of the lithium battery becomes high when the voltage is low, it is not a good manner to charge with large current at the beginning. Otherwise, the battery temperature rises and the battery life is lowered. When the battery voltage is lower than the trickle charge threshold voltage of 3V, the module enters the trickle charge phase, charging the battery at 10% of the maximum charge current up to 90mA, until the battery voltage is higher than 3V.

Once the battery reaches 3V, it will start constant current charge at up to 900 mA, until it reaches the 4.2V cutoff, at which point it switches to constant voltage charge. So it could take a little while for the battery to get back to a state where you can actually draw power from it.
There's apparently a minimum battery voltage of 2.4V, under which output from the battery is cut. If your battery is discharged, with a load connected its output may drop below that even if your battery has been charged a little bit.
Just leave the solar panel connected longer. After a slow charge period until it reaches a safe level, it will start faster charging. Once charged enough you should be back to the initial state.