Really? I don't recall us losing one battle, not one when we had more boots on the ground. It was in the aftermath of Nixon's "Vietnamization" and "Peace With Honor" drawdown and during his Watergate impeachment imbroglio when we lost...(due to the combined fact of the country's war fatigue (because Nixon, and LBJ before him, ascribed the same logic DUH-Bee-Yuh is using) and the results of handing our military operations off to the green, and poorly led RVN forces before they could handle the situation with the more determined NVA).
Don't blame it on Nixon. It was the Dem Congress that pulled the rug out from the ARVN by cutting off funding. The North Vietnamese invaded the South violating the Paris Peace Accords. The US left Vietnam in January 1973. The South hung on for almost two years until they lost our support.