Pololu doesn’t seem to publish max continuous current. Is there somewhere where we can find the gauge of the motor winding for the Metal Gearmotor 12V (#4746)?
We do not provide any lifetime or similar ratings that would make such load ratings meaningful. A general rule of thumb for brushed DC motors like this is to restrict continuous operation to around 25% or less of the stall current.
By the way, there are many factors beyond winding gauge that affect how much current the gearmotor can withstand before incurring thermal damage. Also, the current through the windings directly corresponds to output torque, and for high gear ratios like item #4746, you start hitting the torque limits of the gearbox before you hit the thermal limits of the motor.