Two that I can think of are Iwo Jima and the Battle of Camaron.
The Battle of Camaron was a loss for the French Foreign Legion against the Mexican Gov't, but each year they celebrate this battle, and it is the only battle the FFL treats this way. There is a monument and celebration and all.
Quote from Military.Wiki
"30 April is celebrated as "Camerone Day", an important day for the Legionnaires, when the wooden prosthetic hand of Capitaine Danjou is brought out for display in a special ceremony. The officers prepare and serve the Legionnaires coffee, to celebrate the "...coffee they [The Legionnaires of Camarone] never had." The hand is the most cherished artifact in Legion history:51 and the prestige and honor granted to a Legionnaire to carry it on parade in its protective case is among the greatest bestowed on a Legionnaire."
So this can definitely be a case where the losing party actively commemorates a battle, in fact this is their greatest honor.
The second is the Battle of Iwo Jima and there is a Japanese shrine on Iwo Jima to honor the Japanese that fell at that battle. I have seen it in person. I also believe there are several shrines to honor the dead from the two atomic attacks, though I am not sure that counts as a battle.
The article below mentions the shrine, and though it was a joint ceremony, the shrine is a Shinto shrine to honor the Japanese dead.
"Dock landing ship USS Harpers Ferry (LSD 49) is the backdrop of a Japanese shrine honoring service members lost in the Battle of Iwo Jima. Harpers Ferry is visiting the island to support the 62nd Commemoration of the Battle of Iwo Jima"
source: US NAVY - Story Number: NNS070314-16Release Date: 3/14/2007