As I understand it, The log courthouse at Eminence was burned and the records lost in 1863, local Shannon county histories attribute to the burning to Union activities but I can't nail that down to specific unit or date. What I can say, is the General Davidson's trip in January/February of 1863 found only 2 log cabins, a jail, and the courthouse in the community at the time.

John F. Bradbury, Jr., "'This War Is Managed Mighty Strange:' The Army of Southeastern Missouri, 1862-1863," unpublished paper, Rolla, Missouri, January, 1986, excerpts are here http://www.nps.gov/parkhistory/online_books/ozar/hrs5n.htm#16

From Moser's place names of Shannon County the following comes:
"Eminence

The original county seat, located as early maps show, on Current River. The court house was placed on a fine hill or bluff overlooking the river; hence the name. It was burned during the Civil War and the county government was non-existent for several years; although court was held in Court House Cave (q.v.) during that time. Later the county seat was transferred to the present Eminence (q.v.). The vanished town is now often referred to as "Old Eminence."

The present county seat, located in the center of Eminence Township. It was established in 1870 and has been a post-office since 1874, although the town was not incorporated until 1930. There has been much discussion as to the origin of the name. The obvious solution would be that it was named for its position, but it is located not on an eminence, but in a valley. Jesting neighbors have accounted for the discrepancy by a story to the effect that the first wagon bearing material for the court house broke down at the foot of the hill on which they had intended to build it, and that the inhabitants were too lazy to repair it and hence resigned themselves to living in the hollow. Naturally this explanation is indignantly rejected by natives of the town, as inspired by mere envy and uncharitableness. According to Mr. A. J. Hawkins, the town site was donated by Mr. Thomas Joshua Chilton, who had a large plantation. Mr. Chilton gave 50 acres of land to be dedicated to the public use for streets and alleys, as is mandatory under the Missouri law. This tract extended up the bald hill on the north side of the town, from which point there is a remarkable view. Hence the name. Mr. John Freeman, assistant postmaster at Eminence, says he is the grandson of W. M. Freeman who drove the first wagon-load to build the court house in 1867. He says that the wagon did break down, it being winter and the roads were very muddy, but this incident had nothing to do with the name Eminence. The original intention had been to erect the court house near Round Spring, which is about one mile down Current River, at the place now sometimes called "Old" Eminence, but usually Court House Hollow and Court House Cave. During the 1860's court had been held in this cave at the mouth of the hollow, and had Freeman's wagon not broken down in 1867, the court house building would have been erected there.

Mrs. Cora Williams, who is the daughter of the original wagon-driver, is positive that the name Eminence was transferred from Old Eminence. She says that the old place was so called before the present town was started. It was the original county seat before the Civil War. The court house there was on a fine bluff overlooking Current River. This was burned during the Civil War, and the county government was non-existent for several years. Court was held in the cave during this time. When the court house was rebuilt, it was located at the site of the present Eminence as stated by John Freeman. The court house burned again and was rebuilt. In 1937 it burned once more."

So I think its safe to say the burning of the courthouse is likely the "burning of Eminence" in 1863.

John R