Simonas, the father of Rėklaitis, was married with Teofilė and had nine children – five sons and four daughters.[3][4] Simonas Rėklaitis told his children the history of his family even from the 17th century.[3] According to his father, the Rėklaičiai family came from free peasants and never went to corvée.[3] His parents were educated people, thus all their children graduated from studies.[3] Three of them: Vladas Rėklaitis, Antanas, and Mikas Rėklaitis became officers.[3]
Antanas Rėklaitis brothers colonel Vladas Rėklaitis and division general Mikas Rėklaitis also served in the Lithuanian Armed Forces, all three brothers were arrested by the Soviets following the Soviet occupation of Lithuania in 1940, however they were later liberated and emigrated.[1][5][6][3]
Following his graduation from the Academy of the General Staff of Czechoslovakia in 1933, Rėklaitis served as Commander of the Hussar Regiment, and since 1934 as Commander of the Uhlan Regiment.[1][7] Since June 1934, he was Chief of the Cavalry Staff.[1]
In October 1934, Rėklaitis was transferred to the Third (Operations) Division of the Defence Staff Board.[1]
In 1935–37, Rėklaitis was Commander of the Dragoon Regiment.[1]
Rėklaitis lectured at the War School of Kaunas and the High School of Military of Vytautas the Great.[1] He drafted the Statute of Cavalry Tactics.[1]
Rėklaitis was one of the founders of the Lithuanian Union of Freedom Fighters and the Union of Lithuanian Soldiers Veterans Ramovė, and was the Secretary of the Board of the Ramovė Center.[1] Moreover, he mainted contacts with the Supreme Committee for the Liberation of Lithuania.[1] In 1963, Rėklaitis became involved in the activities of the Lithuanian Front as he was its fund secretary and executive vice-chairman.[1] Rėklaitis collaborated with the magazine Karys, raised funds for its publishing.[1] In 1962, Rėklaitis wrote the book Lietuvių Veteranų Sąjungos Ramovės pirmasis dešimtmetis, 1950–1960.[1]
Rėklaitis died Breese, Illinois, at age 79 after suffering a heart attack at a wedding reception.[9]