Replace C5550 and this should resolve your issue (if you knock something off the board, always check what it is and replace it. It is there for a reason!)
Looking at the schematic, C5550 is on the PP3V3_S0 line for input on U5550. I am not too familiar with this model, since I rarely work on it, but it looks like this circuit is a temperature sensor for the power supply, and U5550 communicates with the SMC via SMBUS_SMC_B_S0_SDA and SMBUS_SMC_B_S0_SCL, then the SMC allows the battery to charge if it has communication with U5550 and the other sensors.
At a guess, I would assume the PP3V3_S0 voltage is not constant and has the occasional dip in voltage due to the missing C5550, at which point it U5550 shorts to ground via the alert pin. The SMC is unable to communicate with this sensor, and therefore doesn't think it is ok to charge the battery. Replacing C5550 will ensure the chip is getting a constant voltage with no dips, so the temperature circuit will communicate with the SMC.
I'm not 100%, but I think this is the general gist of it :)
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