What event weakened the military dictatorship in argentina and brought back democracy after a long absence?

The event that weakened the military dictatorship in Argentina and brought back democracy after a long absence was the Falklands/Malvinas War of 1982 (Malvinas is the Argentine denomination for the Falkland Islands).

Explanation:

The Falklands War faced Argentina and the United Kingdom over the sovereignty of the Falkland, South Georgias and South Sandwich Islands. The war took place between April 2, the day of the Argentine landing on the islands, and on June 14, 1982, the agreed date of the cessation of hostilities in the Falklands, although the British invaded the South Sandwich Islands and on the 20th of June they evacuated the facilities of the Corvette Base Uruguay of Argentina, within the framework of Operation Keyhole.  

The origin of the war was the attempt by Argentina to recover the sovereignty of the islands, which the United Nations considers disputed territories between Argentina and the United Kingdom, although the latter manages and exploits them. Its discovery is controversial; they were occupied successively by Spain, France, Argentina and the United Kingdom (at present). Argentina considers that these territories are occupied by an invading power, and considers them part of its province of Tierra del Fuego, Antarctica and South Atlantic Islands. The final balance of the war on human lives was 649 Argentine military, 255 British and three islander civilians.

In the United Kingdom, the victory helped Margaret Thatcher's conservative government to be re-elected at the beginning of 1983.

In Argentina, the defeat precipitated the end of the Military Junta. Subsequently, in October 1983, elections were held, and in December of that year, a democratic government was installed.  

After more than three decades of the conflict, the United Nations continues to consider the three archipelagos with their surrounding waters as territories with sovereignty as yet undefined, between Argentina and the United Kingdom.