I'm genuinely curious what the northern Arab nations feel about this. What would they gain by including a non-continental African country in their development schemes?
They don't have the comraderie with diasporan black people that subsaharans may possess and these nations have a great deal of say on what goes on at the development bank.
According to the development banks own website, they only included non-African nations in the 80s because those nations were going to add to the money pot. Haiti is not in the same position as Brazil, UAE, or Ireland to add to the AfDB pot. If anything it would dilute the pot.
Furthermore, Haiti is already a borrowing member of the Inter-American development bank making it's access into the AfDB redundant.