Allowing online fraud to happen is one of the surest ways a bank can lose its customers' loyalty, according to a recent survey.

Seventy-one percent of Americans would be likely to switch banks if they became the victim of online banking fraud, according to a survey released Thursday by Entersekt, a banking security company.

However, survey respondents placed a great deal of trust in their banks' fraud-prevention systems: 72% said they were confident that their banks are doing all they can to protect the security of their transactions.

"Banks are in a precarious reputational position with consumer confidence low, accountholder trust high and fraud attacks on the rise in the United States," said Christiaan Brand, Entersekt's chief technology officer, in the news release. "In that volatile environment, one breach, one major hack, one news story on fraud can shatter a bank's reputation, leading to an exodus of customers."

Respondents logged in to their accounts online an average of ten times a month, the survey found. Fifty-eight percent would be willing to use their mobile phones to authenticate online banking activities, such as logins, transfers and payments, the survey found.

The survey, which received responses from over 2,000 U.S. adults, was conducted in May by Harris Interactive.

Entersekt, which is based in South Africa, opened an office in Atlanta and began working with American clients earlier this year. In April, it joined the Fast Identity Online Alliance, a group that is working to develop new methods for digital account verification that would replace the username and password.