WELLS, Maine » It was an unusual sign, even for a restaurant here along the Maine coast, where seasonal home-grown businesses are a way of life.

“;Closed. Gone to try and get a new visa,”; read the hand-scrawled message taped inside the window of Laura's Kitchen, a cozy eatery that specialized in corned beef hash and omelets and where the tiny tables were still set with brightly colored napkins. “;Hope to see you in the spring. Dean & Laura.”;

The sign turned out to be overly optimistic. Dean and Laura Franks, a British couple who opened the restaurant in 2000, found that after nine years of running their business, they could not renew their visa, forcing them to shutter the restaurant and leave the country.

The Franks are among thousands of people who enter the United States each year on E-2 visas, which allow citizens from countries with which the United States has certain trade treaties to invest in businesses and work here. The visas generally are renewed every two years, but there is no limit on how many times they can be renewed. Still, they are not intended as a path to permanent residency or citizenship.

But now, immigration advocates say they are hearing more and more accounts of renewal applications being turned down. It has been an enigmatic process for the Franks, uprooting their lives even though they have paid all their taxes, own the restaurant and its adjacent rental house, and have no debts except a mortgage on their home in Arundel, about 35 miles away.

“;This is the forgotten story of immigration,”; said Angelo Paparelli, a prominent immigration lawyer in California. “;The headlines deal with Arizona and border crossings, but these are real people, too. This is what happens when you play by the rules.”;

In denying the Franks' renewal application last year, immigration officials said their restaurant had become a marginal business. The government sets no specific dollar amount, but it defines a marginal enterprise as one that “;does not have the present or future capacity to generate more than enough income to provide a minimal living”; for the visa holder and his family.

The Franks were surprised and confused to learn last July that they were deemed marginal. Their tax returns show that their gross annual income in 2008 was $64,000, in addition to rental income of $16,800. Their gross profit for the year was $38,800, which was down from their gross profit in 2007 of $50,700 because of the recession, which hit most businesses. They said they barely needed more than enough to provide for minimal living because that is how they live their lives—minimally.

“;We live frugally, we don't drink, we don't smoke, we don't party, and we live within our means,”; Dean Franks said by phone earlier this year from Nova Scotia, where friends had given them use of an empty house. “;We pay all our bills, we don't have car payments, we pay our credit cards off every month, and that seems to count against us.”;

Daniel Maranci, a lawyer in Boston who represented the Franks, said the couple met the test of earning more than enough to make a living because they had enough to hire three or four Americans as wait staff and to pay for their properties.

“;The marginality requirement is fairly subjective,”; Maranci said. “;U.K. nationals are saying there has been a shift generally in the way these cases are being adjudicated, with a more draconian view of marginality.”;

Over the last two and a half years, 8,468 requests for E-2 extensions have been filed, and their approval rate does appear to have dropped, according to figures provided by William G. Wright, a spokesman for the U.S Citizenship and Immigration Services. So far in the 2010 fiscal year, he said, 82 percent of the applications have been approved. In 2009, 84 percent were approved, and in 2008, 91 percent. The service does not track the reasons for denial, so the extent to which marginality was a factor is not clear.

The Franks said the vagueness of the standards made them hard to meet. “;Because there are no hard and fast rules, they can get you on whatever they want,”; Laura Franks said.

Wright, who said he was speaking generally about the process and not about the Franks' case, said that the most recent internal reviews of the decision-making process showed that adjudicators abided by proper standards in 97 percent of cases. “;The adjudicators are doing their job,”; he said.

Paparelli, the California immigration lawyer, said that in recent years, E-2 visa holders were being foiled by a confluence of trends, including an increased vigilance by government officials after the Sept. 11 attacks; a perception by officials that “;evil people”; may be using these visas fraudulently to get into the United States; a bureaucratic disinclination to take the time to examine applications by mom-and-pop operations; and immigration officers' perceptions that local economies already hurt by the recession and job losses could not sustain more businesses.

In England, Dean Franks, 45, had been a financial adviser, and Laura Franks, 42, worked as a chef. But they were not happy and decided in 2000 that they wanted to open a restaurant in Maine, where they spent many vacations and married.

While they came to pursue the American Dream, they said, and wanted to become Americans, they are now fed up with what they see as an arbitrary system that had allowed them to run a business for almost a decade until the day it did not.

“;I can honestly see why people come into the country illegally, because to do it legally is almost impossible,”; Dean Franks said from Nova Scotia.

“;They have tossed us aside like a used tissue,”; he said.

They sought help from local politicians and started a letter-writing campaign. At the website E2Reform.org, they found other British citizens facing the same fate. Learning that some had successfully had their visas renewed at the American Embassy in Barbados, the Franks flew down there. But they had no luck and returned to Nova Scotia, where they sat out the winter.

In mid-April they decided to drive to the Maine-Canadian border, with a letter from their lawyer, Maranci, explaining their situation. After two hours of questioning, they were allowed back into the United States for three months to wrap up their affairs.

They have put the restaurant and the adjoining house on the market for $399,000 and are also selling their home in Arundel, where they are holding yard sales to get rid of their possessions and earn money for food, since they no have no income.

“;We can't do anything until something sells,”; Laura Franks said earlier this month, sitting at an empty table in the dim restaurant, where the plates, cups and cutlery were stacked by the counter. “;All our money is tied up here and in our house.”;

They find themselves without work, without an income and without a country. Gradually, they are emptying out their freezers and working through their larder of cans of assorted foods, leading to what Laura Franks describes as “;some very strange dinners.”; They worry that they will not be able to sell their properties before their time expires, when they expect to go to Canada.

“;I love America,”; Dean Franks said, but he has become embittered because their hard work and frugal ways seem to count for nothing.

“;You can go from 'illegal' to 'green card holder,' but we're going from 'legal' to 'no way you can get a green card,' “; he said. “;We did it wrong. If we came here illegally, we'd have a chance of becoming citizens.”;