How long can you maintain courtyard mulch? ...
Answers: Well, until it decomposes and turns into soil. Basically as long as you want.
Yours is a upright question. Rule of thumb is that mulch should be maintain at a three inch depth to be most effective. That medium that most mulches must be added to at least twice a year within temperate climates (where at hand is no snow) and at least once a year surrounded by colder climates.
If you are using the new synthetic mulch, you buy it and don't hold to replenish for a couple of years--that is because it sinks down into the ground unless there is an underlayment weed cloth below.