Haiti is poorer than any other country in the Americas, but I don't know enough about its history to see what makes it unique among its neighbors. The Dominican Republic, Cuba, Jamaica and the Bahamas are all much stronger economically.
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Was there something unique about French colonial administration in the region which made the area poorer? The other four countries in the region I compared it to were all English or Spanish colonies.
Jamaica and the Bahamas have similar histories to Haiti--they are primarily populated by the descendants of African slaves brought to the islands by European colonizers. But unlike Haiti, those countries earned their independence peacefully, and much later than Haiti. Did Haiti's position as a nation born of a successful slave revolt lead to hostile international relations--did slave holding countries like the US attempt to undermine Haiti?
Pre-revolution Haiti (aka St. Domingue) was actually a very profitable colony for France, with the plantation-based economy bringing in loads of money for the imperial power.
The island's economic downfall was absolutely connected to the successful slave-led revolution. First off, the formerly enslaved people of Haiti were very reluctant to go back to work on large-scale plantations, having been subjected to brutal working conditions for so long. Such economic systems were regarded as key by those in leadership, but the general public had absolutely no interest in returning to that lifestyle. Due to this, Haiti was never able to get back on its feet economically speaking. Further, as you correctly suggested, many of the surrounding slave-holding colonies and nations refused to recognize Haiti as a legitimate state. This led to Haiti's almost complete economic isolation in the years following the revolution. Even if they had been able to reinstate a strong, export-based economy, they would have been hard pressed to find other states to conduct trade with.
Additionally, and perhaps most damaging, was French policy towards the newly-independent Haiti. In exchange for recognition, Haiti was compelled to pay exorbitant reparations to France for losses incurred during the revolution. Of course, these losses included those which stemmed from the institution of slavery, as the formerly enslaved peoples were regarded as lost property. Effectively backed into a corner, Haiti's leadership had pretty much no choice but to accept these demands. This resulted in absolutely crippling debt, which Haiti has never really been able to recoup from. Throw a couple of natural disasters and incompetent/corrupt leaders into the mix, and you end up with Haiti's current economic situation.
If you're interested in learning more on this subject, I'd recommend checking out Laurent Dubois' book, Avengers of the New World, which paints a pretty complete picture of Haiti's revolution and its impacts.