I think most of the warbands would die out, but a few smart ones would eventually evolve in one of several ways.
The first way I can see is for the band to eventually settle down in a well-fortified area and support themselves via farming. However, during bad years or when they have a surplus of people, they send out raids on surrounding communities to gather supplies, loot, and prestige. Kind of like the Vikings, or various tribal populations.
The second way I see them evolving is to become feudal overlords. They set themselves up around a community and decide that it's better to extort 'protection money' from various compound, instead on embarking on risky and potentially fruitless raids. Although they get less supplies in the short run, they have a steady stream of income. Additionally, they have incentive to protect their vassals, since a rival gang or zombie horde would mean they lose their income.
The third option I see is to take inspiration from the Steppe peoples of Central Asia, and become nomadic pastoralists. Wander around the Midwest on horses, bicycles, or whatever forms of transportation can be found, herding semi-feral cattle and occasionally launching raids into the 'civilized' lands. Hell, if you want to go a bit gonzo you could make one band that domesticated a bunch of escaped zoo elephants, and now rides them around like living tanks. Maybe have some outfitted with armor plating taken from old APCs or something.