After July 1863, I assume, since you mention taking it "back"? They didn't have the men and there would have been no point.

After the Confederate forces at Vicksburg surrendered, rather than be held as POWs, large numbers of troops were stationed in camps under the supervision of their own officers as "parolees", meaning they were not supposed to rejoin their units until they had been exchanged for Union prisoners. However, most of them did not hang around as ordered, and huge numbers of them abandoned military service. Entire units melted away to desertion, and it was hard to replace them. Dissent against the Confederate cause grew after the defeats of July 1863 and the population became more resistant to conscription, so raising and equipping a force to replace the troops lost at Vicksburg would have been tough.

A war of attrition was not something the Confederacy could afford, given their starting disadvantage in terms of population and their massive losses through 1863. Additionally, if they had taken back Vicksburg it wouldn't have achieved anything: Memphis, Baton Rouge, and New Orleans were all in Union hands, so control of Vicksburg wouldn't have done much on its own. With the areas upstream and the mouth of the river at New Orleans under federal control there would be no way to get Confederate shipping upriver (and the CSA was always short-handed in terms of ships).

Texas and other areas west of the Mississippi have large populations today, but these areas were quasi-frontier backwaters in 1863 without strategic population centers or any industrial base. The Union controlled the railroads in Mississippi, and there were no major railroads connecting Louisiana, Arkansas, and Texas with Mississippi, so transportation and logistics to support an attack on Vicksburg would have been a problem. As such, after Vicksburg there wasn't any major campaign in the west (other than the pointless Red River campaign) and this area had been cut off from serious action. Cavalry raids against the railroads and Union depots were about all the Confederates could muster in Mississippi.

References (discussion of parolees and desertion): Whittington, Terry. (2002) “In the shadow of defeat: tracking the Vicksburg Parolees” Journal of Mississippi History, 64(4)

Bynum, Victoria, "The Free State of Jones"