"their incapacity" is correct and usable in written English.
You can use it to describe someone's inability to do something. For example, "The students' inability to understand complex mathematical equations was due to their incapacity in the subject."
NEW Yorkers tend to pride themselves on their incapacity for astonishment.
But the great good will of those who volunteered their aid could not make up for their incapacity and incompetence.
The simplest engineering strength criteria are in general not appropriate due to their incapacity in dealing with important size effect induced by stress gradients.
We found functional alterations of this circuit in aged mice that were consistent with their incapacity to update initial goal-directed learning, resulting in faulty activation of projection neurons in the striatum.
The murder of candidates "creates enormous insecurity, which is felt and bemoaned by the public – and it's held up in the faces of the politicians for their incapacity to do anything about it.
"Frustrated by their incapacity to overcome modest opponents in the group phase, senior members of Domenech's squad … decided to take the matter into their own hands and impose self-governance within the French camp.
A longer rehabilitation period for people who have been unemployed could be caused by difficulties in assessing the major cause of their work incapacity, their health impairments or their unemployment situation.
Even if they do an excellent job, such aides are a constant reminder to the sick of their own incapacity, their inability to care for themselves.
In court, Martin has the conviction that most divorces are unnecessary, that people are attempting to escape the inescapable: their own emptiness, their own incapacity to share their lives with another person.
However, it does suggest that we ought to be wary of making sweeping judgements about Asian students and their supposed incapacity for critical thought.
Yet it insists that the denial of rights to children of a certain age on account of their alleged incapacity is simply self-confirming.
