I am also coming to doubt the story of the battery's January 1864 merger with Cobb's Battery. In the battery's muster rolls on Fold3 I find:

February 16, 1864, Dalton Georgia. Voucher for clothing received, 75 Jackets, Capts, Drawers, Shirts, and 75 Pants,

Battery Muster Roll for March and April 1864 Station show Atlanta Georgia. The battery has been stationed at this place since last mustered, The men have been sober and soldierly in their conduct.

Requisition for fuel, 1st Arkansas Battery stationed at Atlanta Georgia, May 1864, 3 officers, 67 Enlisted Men.

Battery Muster Roll for November and December 1864, On Station at Macon Georgia. This company has been stationed at this place since last mustered, It assisted in Repulse of the raid upon this place on the 20th November 1864.

Requisition for Medical Supplies January 10 to Feb. 10, 1865 and again April 1 to 20, 1865, Station, Macon GA. Unit listed as belonging to Martin’s Battalion of Reserve Artillery, C. S.A. was a Field organization composed of independent batteries from various states