Such individuals are often chosen to be on the board for their experience and networking prowess.
It's quite true that testing their mental faculty would be a challenge. Therefore the decision could simply lie with other board members based on their observations of his behaviour and the direct contributions he makes to the company.
Even if they were part if a very very small minority that did (if any exist), it would be hard to test for legally I'd imagine.
We judge people by their pasts, in extreme old age this is no longer applicable.
I do think it's a little sad the obvious has to be pointed out.
If not now, in the future you will have to deal with people getting old, hard truths will have to be dealt with at some point.