Himanshu Sareen was in the midst of building the New York City operation of his 300-employee, New Delhi-headquartered tech company when he got a letter from the U.S. Department of Homeland Security. It arrived in duplicate at home and at work: His visa was not being renewed. He needed to pack his bags.

By just about any measure, Mr. Sareen is the kind of entrepreneurial immigrant the city and the country ought to want. In the middle of 2011, when the letters arrived, the New York City office of Icreon Tech had $3 million in revenue, employed 10 people and had 12 clients.

In the eyes of Homeland Security, “it wasn’t real enough,” he said.

Mr. Sareen managed the new office remotely for a year, until, on reapplication, he was granted another L-1A visa, for executives working for international companies.

He expects revenue of $12 million in the New York office this year. One of his company’s projects, ironically, was working on a system for the Statue of Liberty/Ellis Island.

“Immigration is not an intelligent system,” he said wryly, and noted that he racked up 1 million frequent-flier miles on the 14-hour trips between New York and India.

Though the chances for immigration reform to pass in the newly elected GOP-controlled Congress in the coming months appear slim, the informal campaign is picking up steam again in New York and elsewhere. Advocates are pressing President Barack Obama to make staying here easier for entrepreneurs or people who are in the U.S. under employment visas.

Perhaps because so many undocumented immigrants and people from so-called mixed families of legal and illegal immigrants are sharing their personal stories, more entrepreneurs like Mr. Sareen are speaking out. While the stories of the children on the southern border of the U.S. rend hearts, it’s the experiences of entrepreneurial immigrants that could result in meaningful reform, even this year.

“Initially I was a little scared,” said Atulya Pandey, a native of Nepal who is a co-founder of Pagevamp, a three-year-old Manhattan-based company that employs six. “But now I talk to people in my co-working space regularly, and whenever there are events I try to get people to come to be educated.”

Mr. Pandey is active through FWD.us., a high-profile immigration-reform group that has established a New York City chapter and now has 30,000 supporters in the metro area. FWD.us is backed by Silicon Valley’s biggest names, including Microsoft’s Bill Gates, Facebook’s Mark Zuckerberg and LinkedIn’s Reid Hoffman. There are a handful of New Yorkers on its list of major contributors, including Fred Wilson and Barry Diller.

Decade-long waits

The advocates are pressing for what’s known as administrative action, rather than broad legislative reform. Mr. Obama could make some changes through the Department of Homeland Security bureaucracy, such as making more green cards available or altering the rules so that dependents of visa holders don’t count toward quotas.

The system is cumbersome at best. Professionals, including doctors and highly skilled engineers and executives, wait for as long as a decade to obtain a visa if they are from countries such as India or China. Businesspeople who want to establish companies here, or immigrants who are already here and want to launch firms, typically don’t face long waits, but they do have a dizzying array of options—and there’s risk involved in all.

For instance, an entrepreneur from another country could get a green card, becoming a permanent legal resident, by agreeing to invest $1 million “in a commercial enterprise” and create 10 jobs, according to David Leopold, a past president of the Washington, D.C.-based American Immigration Lawyers Association.

If a business didn’t meet those criteria, the entrepreneur would have to return home. It’s particularly difficult to get a renewal of an L-1A visa, the kind Mr. Sareen had, immigration attorneys say.

“Why would you come here if you run the risk of losing your investment?” Mr. Leopold asked.

Any kind of reform could have a big impact locally.

New York City has long been a haven for immigrants. In 2010, 31.2% of all business owners in New York state were foreign-born, according to the Washington, D.C.-based Immigration Policy Center, a nonpartisan organization. That number rises to 36% in the New York City metropolitan area. These businesses had a total net income of $12.6 billion, representing 22.6% of all net business income in the state.

Lobbying for reform

Immigrant-owned firms are aided by formal and informal city policies that aim to treat the large population of foreign-born residents just like any other New Yorkers. The latest example: an initiative to create a municipal ID card that could enable even illegal immigrants to open bank accounts.

Among local entrepreneurs lobbying for reform is Madhav Krishna, a native of Delhi who came here to attend Columbia University, graduating in 2008. After years of encounters with the immigration system, he has become an acolyte for FWD.us in the past year, attending meetings and informing others, such as his partners in a startup launched in January, about immigration issues. “My American co-founders had no idea the system worked this way until I explained it,” he said.

Mr. Krishna has his own firm, mESL, which employs three people part-time to work on an app to help teach English. But to maintain his green-card status, he keeps a day job in advertising tech company ADstruc. For FWD.us, he is working on an app that might help tell stories of people caught in the system.

“I think about it every night, every day, how much further along I would be if I could work on my company full-time,” he said.

What may finally push some immigration reform into reality is the burgeoning influence of Asian immigrants. Asians became the fastest-growing immigrant group in the U.S. almost a decade ago, according to the Pew Research Center. Among those ages 25 to 64 who have arrived in recent years, 61% have at least a bachelor’s degree. This is double the share among recent non-Asian arrivals, and almost surely makes them the most highly educated cohort of immigrants in U.S. history, said the report.

These immigrants are making their mark in entrepreneurship. Asian-immigrant-owned businesses in New York City had average annual revenue of $292,000, versus $96,000 for native-born entrepreneurs, according to an analysis of financial data by Manhattan-based Biz2Credit of 18,904 companies that applied for loans on its platform between Jan. 1, 2013, and Oct. 14, 2014. The company connects small businesses with lenders, including banks and other funders, via an online platform. The average credit score of businesses owned by Asian immigrants was 664, versus 627 for U.S.-born owners.

Mr. Pandey said he could have gotten a much higher-paying job after his graduation from the University of Pennsylvania, but he was too drawn to entrepreneurship. Mr. Pandey’s Pagevamp gives users an inexpensive way to maintain websites by using Facebook to manage them. He and his co-founders met on -moving-in day in their college dorm. He is legally in the U.S. because he is still a student, taking one class a week at a vocational school.

“My struggles within the immigration system involve more than just my own experience: They involve my colleagues and the business that we’re trying to build and grow,” he said.

A version of this article appears in the November 10, 2014, print issue of Crain’s New York Business as “Immigrant-owned firms fight to stay put”.