Why do operational amplifiers have an output current limit?
The output current that your op amp is able to source is determined by IREF and the size ratio of Q7 and Q8. The maximum output current is sourced when Q4 is in triode and Q6 is in cutoff.

The output current that the op amp is able to sink is more complicated, since it will depend on the common mode input voltage, but it happens when the gate of Q6 is pulled high by driving the non inverting input below the inverting input.

Usually that is an op amp you will find inside an IC and if it has to source current, that current has to come from the bias current. Usually commercially available op amps have an output stage, usually class B or AB, which buffers the high impedance output of the previous stage and is able to supply mA of current.