According to the Hanafi school, Zakat is not obligatory on an individual who continuously lacks mental capacity. The other schools have differing views on this, and are of the opinion that Zakat is obligatory on the wealth of such a person.
The Hanafi school are of the view that a person with continuous mental incapacity is exempt from Zakat. An example would be someone who lost their memory from Amnesia, or is medically diagnosed with a condition due to which they are unaware of what they are saying or doing, and are therefore not entirely responsible. However, a person with intermittent mental capacity is still required to pay Zakat.