Oh, we have actually lost quite a few. Especially in Vietnam.
Paul Revere IV comes immediately to mind. After a fruitless search and destroy mission along the Cambodian border, a company sized force was ambushed by a battalion of NVA, destroying two platoons before fading back into the jungle.
And the Battle of Xa Cam My, where once again a Battalion of NVA was able to isolate a US infantry company and almost totally destroy it before fading into the jungles yet again.
And then there was Operation Hickory, where a Regimental sized Marine force struck across the border just north of the DMZ. And what followed was 10 days of battle, with the NVA withdrawing each time contact was made, only to attack again from an unexpected direction. The Marines would take a bunker complex or hilltop with almost no opposition, only to be attacked in the evening and have to fight for their lives until morning when the NVA once again faded into the jungle. After a week and a half they finally left, with over 140 Marines and Corpsmen dead, and almost 900 wounded.
Oh, the US lost a great many battles in Vietnam, well over a hundred of them.
And hell, we have not only the Battle of Mogadishu, but other battles in Iraq and Afghanistan we have lost. Operation Red Wings springs immediately to mind, where we lost not only a SEAL team but multiple helicopters and other losses before the enemy faded into the mountains. Or the Battle of Wanat, the Battle of Najaf, the First Battle of Fallujah, Donkey Island, and others ranging from the Good Friday Ambush in 2004 to several of the wide spread battles that made up the Battle of Nasiriyah (including the destruction of the 507th Maintenance Company.
Oh, the US is not invincible and has unquestionably lost battles. Some of them actually not all that long ago. Then there were also some that were recorded as "victories", but at the very best they were pyrrhic victories as the US might have won a tactical victory, but strategically they lost.