Is it true that the US never lost a major battle in Vietnam?

Yes, it is true that the U.S. never lost a major battle during the Vietnam War (note, though, that there were engagements in which the ARVN, fighting on its own, was defeated by the Communist forces). One of the most frustrating legacies of the Vietnam War is the misconception that the U.S. military "lost"; in actuality, the U.S. won every major engagement and maintained a 5:1 casualty ratio throughout the war. A prime example of the kind of myths that surround Vietnam is the Tet Offensive, which many incorrectly think was a Communist victory because of Walter Cronkite's infamous (and inaccurate) editorial at the time; in actuality, the Tet Offensive was a decisive military defeat for the Communists. Despite U.S. victories in all the major engagements, the North was ultimately able to win the war by essentially waiting out U.S. involvement. A sizable segment of the American public began to conclude that the war wasn't worth the cost and support waned, dividing the country and pressuring the government to pursue a policy of "Vietnamization" under which American troops were withdrawn while the ARVN was built up so it could assume responsibility for defending South Vietnam itself. Once U.S. involvement ceased in 1973, it was a formality that the South would fall, which it did in 1975.