Justin,
Lieut. Col. Henry K. Brown (formerly captain of Co. G) declined to run for reelection during the regimental reorganization at Camp McIntosh, near Corinth, Mississippi, on May 8, 1862, due to his advanced age (55). He subsequently resigned, effective May 23, 1862, and returned to Sevier County, Arkansas.
The only Captain Brown, of Arkansas, who was killed in action was, so far as I know, Capt. Hugh Thomas Brown, Co. G, 3rd Regiment Arkansas State Troops, who was killed while leading a charge at Wilson's Creek (Missouri) on August 10, 1861. There are several eyewitness accounts of his death, which was nothing short of heroic. A new company of infantry organized the next year was named the Brown Guards in his honor.