People came back from America all the time because the situation back home had improved for them, they couldn't make it in the New World (or in fact they had made it big and could afford to return in a grand way), or they were plain homesick. It was probably a miniscule share of all emigrants, but not unusual.
Found this listing of reasons people returned. It tracks with what I remember from a class I took on the history of US immigration.
Birds of Passage The reasons for returning home are as complex as the human mind. Some returned in what they considered triumph whereas others went home in defeat. Some never intended to stay in America permanently. We may think that "guest workers" who come for temporary work are a recent phenomena but they are not. The Italians were accustomed to moving about Europe in search of temporary work and many came to the United States with that in mind. They wanted to work for a season or two and make enough money to buy a farm back home. They never intended to stay. These short-timers were sometimes known as "birds of passage" and were often resented by Americans.
Retirement Even those who stayed in America many years may have retired to the homeland. With a small savings they could live well and be looked upon with respect by the villagers since they had lived in America. Many, especially Italians, wanted to return home to die so they could be buried in the family churchyard. Often the elderly parents would return home but their descendants stayed in America.
The Marriage Market Since the dowry was very much alive in many parts of Europe and emigration had reduced the number of eligible males, many women came to the United States to earn some money to improve their position in the marriage market. Marriage was very much an economic arrangement between two families and a woman's social position, physical comfort and standing in the community for the rest of her life depended on having enough assets to be considered a desirable match by a young man's family. If she could work for two or three years, she could return home in a much better bargaining position.
Nostalgia For some the American dream just didn't work out. They got discouraged and went back. However, many of these people found that their memories of home had been viewed through rose colored glasses and they were equally unhappy with their old problems. They had become more American than they realized and found there was a lot of good to be said of their new country. Some of these people eventually immigrated to America a second time.
Economic Depression and Family Obligation A countrywide economic depression also caused many to return. Problems with the family left behind was also another reason for returning, but this would probably only be temporary. Some women had to return to take care of a sick parent. When they left the US they may not have known whether they would stay permanently in the old country or return to the US.
Diversity or Chaos? Some found America too diverse. They liked the familiar rules and setting where people spoke the same language, attended the same church and conformed to the same standards. They also hated seeing their children growing up as foreigners to them. However, trying to return these children to the old customs was usually a losing battle. The children either stayed in the U.S. when the parents returned or they came back as soon as they were of age. More affluent immigrants might have felt that America had no culture and preferred the refinements of the old world. As with those whose return was driven by nostalgia, these people also often found there was much to admire about the new world with its energy and freedom.
Unwilling Emigrants In England the local authorities were responsible for taking care of the poor. In some cases they decided the best solution for the indigent was a one way ticket to America. Since these people were unwilling emigrants in the first place, they might return home as soon as they had earned enough money to pay their passage.
No Pioneer Spirit Some immigrants just did not have the personality required to uproot their lives and settle in an entirely new, and sometimes hostile, environment. It wouldn't have mattered where they went. They were simply unhappy outside of their familiar setting.