The June 30 to Aug 31,1862 muster roll shows he was last paid June 30, [1862], his brother/cousin Sgt. Jefferson Keeton, Co. I, was also paid on that date, and then again on Aug. 31, 1862. This would indicate that John was sent to the hospital sometime in July or August, 1862. After Pea Ridge, March 7/8, 1862, the regiment served during the Corinth, Miss. campaign*, believe April 29 to June 10, then arrived at Louden, East Tenn., either before or after, participating in the battle of Richmond, Ky Aug. 20/30. I suspect he died in a hospital in the Corinth, Iuka area. My picks would be Lauderdale Springs, Okolona, or Meridian. Below, I list men who died about this time, list taken from five of the companies of the regiment. Same source as the URL below. The regiments and Company I muster rolls do not provide the intelligence as to where they were located during this period.
* http://www.couchgenweb.com/civilwar/4mcnair_f&s.html
Died before 30Aug1862 in hospital at Okolona, MS.
Deserted 2Jul1862. Died in hospital. Date & place unknown (Possibly Lauderdale, MS).
Died 1May1862 at Panola, MS
Died 30Jun1862 in Brookeville, MS
Died 17Jul1862 at Lauderdale Springs, MS.
Died 12Jun1862. (One record shows 12Jul1862 at Brookville, MS).
Discharged 16May1862. Died 1862 in hospital at Okolona, MS.
4th Regiment, Arkansas Infantry
4th (McNair's) Infantry Regiment [also called Southwestern Arkansas Regiment], assembled at Miller's Springs, Lawrence County, Arkansas, recruited its companies in Calhoun, Hempstead, Lafayette, Montgomery, Pike, and Polk counties. After fighting at Elkhorn Tavern, the unit was sent to Kentucky where it was active at Richmond. It then was assigned to General McNair's and D. H. Reynold's Brigade, Army of Tennessee. Soon after the Battle of Murfreesboro, the 4th Arkansas Battalion merged into the regiment and in August, 1863, the 31st Arkansas transferred to the 4th. It was involved at Jackson, participated in the campaigns of the army from Chickamauga to Atlanta, saw action in Tennessee under Hood, and was engaged at Averasboro and Bentonville. This unit was organized with 695 men, and reported 55 casualties at Elkhorn Tavern, 23 at Richmond, and 79 at Murfreesboro. The 4th/31st/4th Battalion lost twenty-four percent of the 385 engaged at Chickamauga. Few surrendered on April 26, 1865. The field officers were Colonels Henry C. Bunn and Evander McNair, Lieutenant Colonels James H. May and Samuel Ogden, and Major Jos. B. McCulloch.
http://www.itd.nps.gov/cwss/regiments.cfm
Two months ago while at the National Archives in Washington, DC, I tried to find a patients records in a Lauderdale Springs, MS Prescription Book. It was nigh impossible. A huge heavy ledger with no page annotation, ink rather faint, difficult to read. Would take a considerable amount of time to study, and then, results uncertain.