It persisted on the eastern part of the island but not in Haiti. After the revolution ended around 1804 with the independence of Haiti, the eastern part of the island, the traditionally Spanish Colony and what is now the Dominican Republic remained under French rule, and thus slavery was maintained. It bears to note that the slave population on the eastern part was much smaller as the colony had relatively no plantations compared to the very rich and productive former French colony of Haiti.

The Black Jacobins - C. L. R. James The Dominican Republic: A National History - Frank Moya Pons

the institution of slavery persisted on the island after the French were forced off

Are you talking about the Spanish side of the island (modern-day Dominican Republic)? The persistence of slavery in the colony of Santo Domingo (the former name of Dominican Republic) wasn't a sign that the Haitian Revolution didn't succeed. You have to remember that Haiti (St. Domingue) and the Dominican Republic (Santo Domingo) were two separate colonies. Haiti was ruled by France and Dominican Republic by Spain. The Haitian Revolution was a slave revolt in what is now Haiti and it succeeded in its goal of freeing the slaves there. Santo Domingo was drawn into the Haitian Revolution, but it wasn't the center of it. The slaves in the DR were eventually freed by the Haitians, presumably when the country was occupied by Haiti in the 19th century.