The United States army has lost several wars.
Since the early 50s the US army lost or withdrew from following battles with no or little success.
Korean War, Korea 1950-1953
Second Indochina War, Vietnam 1953-1975
Bay of Pigs Invasion, Cuba 1961
Operation Restore Hope, Somalia (Multinational for US victory later) 1992-1994
There are also several wars going against different groups and organizations.
War on terror (al-Qaeda, Taliban, Al Shabaab, Hamas, Hesbollah etc.) 2001
LRA Insurgency, Central Africa 2011