There are a few different issues at play with Haiti, but the short answer is a complicated history of colonialism, slavery, and racial tensions that were uniquely damaging to the nascent Haitian state.

Whereas Haiti was the second independent nation in the Americas, the nations who secured independence after Haiti did so in much different paths. The United States secured independence with the help and recognition of France and Spain, and most of the colonial administration pre-independence remained in control after independence. While there were certainly adjustments, the leaders and power bases before and after American independence were largely the same. Other prominent breakaway factions accomplished the same: Simon Bolivar and his independence campaign exploited numerous existing administrators with sympathies towards independence, Brazil was de facto independent and at one point the actual seat of power for the Portuguese monarchy (who fled Europe during the Peninsular War), and the Dominican Republic had a number of issues on their path to independence but enjoyed protection by the United States during the last stages of independence.

Haiti enjoyed none of this. The Haitian revolution was led in first stages by Toussaint Louverture, who was a freed slave and had little experience or political connections to rely on. He was tricked into meeting with the French under pretense of negotiations, at which point he was arrested in 1802 and died less than a year later in a French prison. Jean-Jacques Dessalines, another freed slave, largely took control of the Haitian revolutionary forces and established an independent Haiti in 1804, before being assassinated in 1806. Prior to his assassination, Dessalines ordered a mass killing of French citizens residing in Haiti, with at least 3,000 French executed and many thousands more fleeing to the United States.

There were several consequences of this mass-killing, and of the general political disorder of both Loverture and Dessalines being removed from power in hostile manners in short period. The first is that the new state of Haiti was, rather uniquely for the various colonial nations that would pop up in the coming years, almost entirely devoid of Europeans. Some were spared, mostly Polish residents who had supported the revolution, but those not killed had fled. This was quite damaging as the remaining residents were largely former slaves who lacked the same education as the white citizens and the racial tension was worsened by these acts. Further, the mass execution and tales of the residents who fled to the United States inflamed the slaveowners of the South and created a paranoia about a potential mass slave revolt and mass killings of white southerners as happened in Haiti -- such paranoia continued well into the United States Civil War, with Confederates and Confederate sympathizers warning of "the horrors of St. Domingo" in the early years. This led to policy of isolation, began in 1804 by President Thomas Jefferson, and Haiti would not be officially recognized as an independent nation by the United States until 1862.

While all of this was damaging enough, the isolation also opened the door for diplomatic extortion of the Haitians. In 1825, the French government sent numerous warships to Haiti demanding the former colony pay an indemnity of 150 million francs for the property lost in the revolution (that is to say the slaves who had revolted against them) in exchange for diplomatic recognition. To pay the indemnity, the Haitians had to take out exorbitant loans, sometimes at interest as high as 18 per cent per annum, and as a consequence of having no international recognition were obligated to take these loans from the French (and later the United States) as no other countries would treat with them. It is estimated that by the late 1800s, some eighty percent of the total Haitian revenues were being diverted into French indemnity payments, and the French during this period maintained control over the entire Haitian treasury, which they forced to be located in Paris until the official government debts were paid back in 1893.

But while the French indemnity was repaid, this was still only part of the issues facing Haiti. The other issue was that even after fears of a slave revolt were quelled, the United States remained belligerent at best towards the Haitians. Andrew Johnson in 1868 had plans made for an annexation of Haiti by the United States, and in 1890 the United States sent a fleet of warships to Haiti in an attempt to pressure the Haitians to "lease" a port to the United States. Newly elected president Florvil Hyppolite refused the demands, which angered the United States (and led to them insisting that the warships sent to Haiti were merely for peaceful negotiation, not for any threat of violence.) Haiti's troubles continued when the Germans in 1897 demanded a pardon for German national Emile Luders, along with a formal apology, an indemnity, and a host of other embarrassing demands, backed by yet another fleet of warships. This became an issue as the United States viewed the Luders affair as a sign German influence had grown too strong in Haiti. Political instability during the following years eventually prompted US businesses to lobby the government to intervene in Haiti, an intervention that was granted by Woodrow Wilson in 1915. American marines occupied Haiti and established a military regime with a puppet government.

The changes brought about by the American occupation were extreme. Where the Haitian constitution had previously banned all foreign nationals from holding property, the US occupation transferred control of all customs houses, banks, and treasuries (along with associated financial and administrative institutions) to the United States. About 40% of the Haitian wealth was seized by the United States and used to pay off loans to American banks that had been used prior to pay the French indemnity. The United States had final say over all expenditures by the Haitians, and was granted by treaty control over all foreign relations and economic affairs for ten years, later extended to twenty. When the Haitian legislature refused to ratify the new constitution being forced on them in 1917, the United States occupying forces dissolved the legislature and did not allow a new legislature to meet until 1929. At this point, prominent black Americans began protesting, with W.E.B. duBois and the NAACP decrying the conditions in Haiti. The United States occupation had effectively reversed older racial politics and granted rights to the mulatto class while suppressing the Afro-Carib classes that comprised the majority of the Haitians. Conditions continued to deteriorate as the US puppet regime began a forced labor policy in Haiti, requiring Haitian citizens to work on various "economic" projects without compensation and resulting in a large number of deaths from overwork. These deaths also were joined with the large numbers killed by US forces during revolts against the occupation.

Finally in 1933, the situation had become so untenable that the United States began withdrawing from Haiti and returned control back to the Haitians. However, the United States continued to enforce the treaty stipulations that gave them financial control until debts were repaid, which was maintained until the final payments in 1947. During this final stage, the portion of Haitian revenues going to foreign debt payments still accounted for 20% the total. While the occupation did result in some infrastructure and economic reforms, the end result was not that glowing either: Haiti's education system was essentially dismantled, replacing prior comprehensive education with a strict vocational system that only taught agricultural practices and siphoning even more money from Haitian institutions in those set up by the United States. Segregation had been imported from the American South and enforced in Haiti, and altogether somewhere between 3,000 and 15,000 Haitians died during the occupation.

So to give a condensed answer: a combination of French and United States hostility toward Haiti, and extortionate policy toward the island, effectively deprived Haiti of almost 125 years of economic development that they only began to recover from in 1934 (after the occupation ended) or later in 1947 (when the last of the indemnity-related debts were paid). While the colony was rich and fairly well situated, the indemnities siphoned almost all of this wealth into the hands of French and American banks while keeping the new country from actually investing its wealth.

I’m kind of surprised there isn’t a more recent answer to this, but this comment has collected some past answers