Francis used to be a VP at Fairfax and sat on the investment committee. At that time, Fairfax had put some money into Francis' funds and Francis decided that it would be a conflict of interest to stay on while managing money separately for Fairfax.
I think the same issue would come up if Francis sat on the board. If at some time, he no longer manages any money for Fairfax, as he is independently wealthy, maybe they will ask him to join.
Regardless, he's still there as an advisor or sounding board to Prem whenever Prem needs him, and I would suspect any future board without Prem would feel the same way, especially since Prem's children are on the board now. Cheers!