I would believe he was lost during the Atlanta campaign. See below:

Record of Events for Thirty-third Regiment, Mississippi Infantry, Company E

March-April 1864. Stationed near Montevallo, Alabama,
April 4.— Left Demopolis. Marched to Montevallo, distance
eighty-five miles.
3rd Corporal Hiram G. Ware, Present [No further records]

May-June 1864.
[Muster Roll missing]

Engagements: New Hope Church, GA May 29
?? May 31

July-August 1864.
Stationed at Atlanta, Georgia,
The company has been in all regular engagements. Three
men killed on the field; four commissioned officers and nine men
missing; and four men wounded and sent to the hospital. A por-
tion of the company has been skirmishing every day, except four
or five. Marched about twenty-five miles since last muster.

Engagements: Peach Tree Creek, Ga. July 20 & 23
Jonesboro, Ga. Aug. 31

Sources used by Historical Data Systems, Inc.:
- Index to Compiled Confederate Military Service Records