This is from a paper on the American OBD 2 standards. The system in other regions may not be so strict however you can see from this that if the fault relates to a "malfunction" of the catalytic converter, at least on systems intended to comply with the USA standard, the MIL light will not re-set itself. I have added the underline.
Typically the “check engine” light on the instrument panel is illuminated whenever any fault occurs. For emissions related faults the MIL light will not go out until cleared from memory by the mechanic. For non-emissions related faults the MIL light goes out automatically if the malfunction clears. However the PCM stores the DTC associated with the detected failure until the diagnostic system is manually cleared or until a specified number of engine cycles (twenty) occur with no malfunction. For some DTCs (of lesser consequence) there is no activation of the “check engine” MIL light.
In some cases the number of cycles (trips or ignition on/off) may be less than 20, as low as 3, for the MIL light to go out for non-emissions related faults but the fault remains in memory for a period.
If anyone wants to wade through many pages of information there are explanations here in a reasonably understandable form of how the whole OBD 2 system works.
Introduction to On Board Diagnostics (II)