There is no record of his status after the September 1862 muster. There is one subsequent muster roll for the period December 31, 1862 to April 30, 1863 which was dated August 17. Not being mentioned could mean he had been dropped from the rolls for some unknown reason. This could have occurred on the missing Sept/Oct, 1862 bi-monthly muster. And then, he could have later rejoined his unit. Do you know if he survived the war?
William McBee, Private, Company Fk, 11th Regiment Arkansas Infantry, enlisted August 22, 1861 at Little Rock, recorded at the September 22, 1862 muster as, absent, sick at our capture, present locality unknown, no further records
Compiled Service Records of Confederate Soldiers Who Served in Organizations from the State of Arkansas
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McBEE, WILLIAM Pvt
Enl 12Aug1861 at Little Rock, AR. Absent when the 11th was captured 8Apr1862 at Island 10, MO. Locality unknown.
http://www.couchgenweb.com/civilwar/11thcof.html
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The regiment was ordered to Fort Pillow, November,
1861, and was brigaded with the Twelfth, commanded by
Col. E. W. Gantt; was stationed at Island No. to on the
Mississippi river, and transferred back and forth to New
Madrid at the will of Gen. Gid. J. Pillow, who had very
impracticable ideas of the war we had entered upon.
Island No. to was surrendered April 15, 1862, after a ter-
rific bombardment by the enemy's mortar-boats and gun-
boats, aided by an overflow which nearly submerged the
island. The Confederate defenses consisted of dissolving
earthworks and twenty guns. Maj. W. J. Hoadley, of
Little Rock, having served his guns with great bravery,
spiked them and made his escape with one section of the
battalion. The others were included in the cartel, and
were transported to Camp Butler near Springfield, Ill.,
then to Camp Chase (Chicago), the officers to Johnson's
island, Lake Erie. Lieutenant Gibson, of Company H,
was shot dead on Johnson's island by a Federal sentinel
because he crossed the "dead line." The two regiments
were exchanged September, 1862. The year of the first
enlistment expiring there was a reorganization,
Source: Confederate Military History, vol. XIV, p. 308
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The 11th Arkansas Infantry (1861–1865) was a Confederate Army infantry regiment during the American Civil War. Following the units surrender during the Battle of Island No. 10, it was consolidated with Griffiths 17th Arkansas Infantry Regiment and mounted. Following the surrender of Port Hudson, some unit members returned to Arkansas and became part of Poe's Arkansas Cavalry Battalion and Logan's 11th Arkansas Cavalry Regiment.
Some members of the 11/17th Consolidated Arkansas Mounted Infantry were captured at the Siege of Port Hudson on July 9, 1863. These men were later released and exchanged in Arkansas and many would later join Poe's Arkansas Cavalry Battalion
https://en.wikipedia.org/wiki/11th_Arkansas_Infantry_Regiment