It's quite common to vary between farming and hunting-and-gathering, and also very common to hunt and gather in addition to farming. In times of trouble or when the system breaks down, people tend to move away from urban centres and may start hunting and gathering. That said, I can't think of any specific examples right now. Mostly I came to say that the development of agriculture is one of the big questions in archaeology, so you should ask this over at /r/AskAnthropology. Some people there might have more information.

There's a great book called "After the Ice" by Steve Mithen that answers this question in one of the chapters. The book is a standard in archeology classes across the U.S. Some people have already responded about switching back during the transitionary period from agriculture to hunting-gathering, so I'll address briefly address societies that had made a "full" transition. Essentially, the societies primarily switched back to hunter gathering if they were coastal based - the bounty of the sea close to providing the same caloric value as agriculture without the same intensity of labor. This perhaps explains why some of the earliest urban centers (Babylon, Indus Valley) developed around rivers inland, rather than on the coasts. Archeological evidence indicates that agriculture techniques spread in similar ways to material culture. As such, any inland group that made a switch back to hunting and gathering would often be pressured to either revert to agriculture or be assimilated into agricultural societies.

In 1491 by Charles Mann, the author discusses the Pre-Columbian Amazonian societies, the Amazon apparently has massive evidence of being heavily altered by humans. It's not true farming, and the people who did it are categorized as hunter-horticulturists, but after epidemic disease destroyed these societies, the remaining peoples were hunter-gatherers.

But that makes me think of the Maya that remained that in the southern Maya lowlands. Classical Maya civilization was urbanized with intensive farming. After the collapse, the southern Maya lowlands were incredibly depopulated, but there were peoples who remained in that area. My impression of those Maya is that they were hunter-gatherers vs. the highlands and Yucatan Maya which continued agriculture. But that might just be the post-apocalyptic trope in my head. Did the Maya remaining in the Classical heartland revert to hunting and gathering?

Great answers here already, I just wanted to link another reference that OP may be interested in: The Art of Not Being Governed by James C. Scott.

Historically hunting buffalo, the iconic food source of Plains Indians in modern minds, was a difficult prospect. Due to this American-Indian cultures located around the south plains, such as the Apaches, were mainly semi-sedentary agriculturalists, taking advantage of farming in a similar fashion to their neighboring Pueblo societies. It was only with the introduction of the horse after the arrival of the Spanish that this began to change. The mobility and speed granted by the use of horses made it possible to effectively hunt buffalo. Obtaining food from hunting buffalo was more time and energy efficient then farming causing Apache groups to begin to give up farming in favor of focusing on hunting and gathering. The Comanches adoption of the horses for military uses, which allowed them to expand into the south plains and force the Apaches out of their traditional area, solidified the Apaches move away from farming and into a pure hunter-gatherer lifestyle.

The Comanche Empire (2008) by Pekka Hämäläinen

The Comanche: Lords of the Southern Plains (1952) by Ernest Wallace and E. Adamson Hoebel

They didn't go back to being fully hunter-gatherers, but the populations of the Mississippian cultures in the Southwest United States went from being settled agriculturalists living in cities, to semi-migratory, because of climate change and then later the impact of European diseases causing people to flee the cities.