Why continue to hang onto it then if it's such a burden?
Legally, the U.S. Constitution grants Congress (not the president) authority over U.S. territories,* but a series of statutes and executive orders have essentially left the decision regarding Puerto Rico's fate―national independence, statehood, or continuation of territorial status―to the residents of the island.
Politically, the situation is complicated, both for Puerto Rican residents and for mainland politicians. Puerto Ricans are citizens of the United States, but as residents of a territory they lack certain rights (e.g., they can't vote in presidential elections) and have certain privileges (e.g., most residents of Puerto Rico are exempt from federal income taxation). In other words, there are benefits and detriments to acquiring either national independence or statehood, and so far neither option has been able to command clear majority support from the island's residents.
Congressional opinion is also divided on the long-term status of Puerto Rico. As citizens, Puerto Ricans are free to relocate at any time to any state. This can alter the political balance in states where elections tend to be decided by small majorities or pluralities; for example, it is generally believed that migration of Puerto Ricans to Florida benefits the Democratic Party in that state. Members of Congress from both major parties frequently have expressed the opinion that as a state, Puerto Rico would tend to favor Democratic over Republican presidential candidates and would be more likely to elect Democratic members of the House of Representatives and the Senate.
Absent a consensus in Puerto Rico or in Congress, the default option has been to leave the island's current status undisturbed.
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* "The Congress shall have power to dispose of and make all needful rules and regulations respecting the territory or other property belonging to the United States." (U.S. Constitution, Article IV §3.)
