I got in touch with LATAM via Facebook. The booking agent said that the flight is full, however any direct AQP CUZ flight you pick in January has the same issue, so I suspect the agent is incorrect. Not sure what else to do with LATAM...

There is a Peruvian flight we can get the following day at a similar time. A bit frustrating to have to go with another carrier when there is a flight showing with LATAM but not sure what else to do.

Thanks
AI