Strung across the front of the St. Rita of Cascia Church rectory in the Mott Haven section of the Bronx this week is a banner with Pope Benedict XVI’s image superimposed over a photo of the church’s squat, one-story sanctuary.

Behind the pope’s raised arms are immaculate white-washed walls and a red-tiled roof, which could give the impression he is visiting a church in one of the Latin American countries that St. Rita’s mostly Hispanic parishioners call home, not an especially rough corner of what may be the most impoverished congressional district in the nation.

The banner reflects the wishful thinking of the church’s priest that the pope might make a detour this Sunday on his way to Yankee Stadium a few blocks away, as his predecessor, Pope John Paul II, did during a trip to the Bronx in the 1970s. But with security concerns now at an all-time high and because of the neighborhood’s particularly negative reputation for violence and drug crime, the Reverend Jose Gutierrez and his parishioners realize their dream is unlikely to be fulfilled — no matter that St. Rita is the patron of the impossible.

If Benedict were able to venture out to see St. Rita’s on his trip to meet his American flock for the first time, he would find a parish whose struggles have come to reflect some of the larger problems confronting the Catholic Church as a whole.

He might also discover the key to the Catholic Church’s continued hope and vibrancy even as it faces challenges.

“It’s a poor parish, but this doesn’t impede us,” Rev. Gutierrez said.

The neighborhood hasn’t changed all that much since the day John Paul visited in 1979 to bless a low-income housing development on Morris Avenue. In the 16th Congressional District, which includes St. Rita’s, more than 40% of the total population and 54% of children live below the poverty line according to 2006 Census data.

The Reverend Ramon Manrique, another of St. Rita’s priests, said he sees the statistics come to life each day for the families in his church, which sits in the shadow of a phalanx of gritty public project towers.

“It’s an area with a lot of drugs, and families are destroyed. So many are broken. There’s alcohol, and there’s a lot of suffering,” he said.

Although about a fifth of the laity in the American Catholic Church as a whole is wealthy, a third of American Catholics makes less than $30,000 a year, and another fifth makes less than $50,000, according to a 2007 Pew Research Center report. In addition, the Catholic Church itself has had to tighten its belt in recent years by closing parishes, including some in the South Bronx, as money has drained away following the clergy sex abuse scandal; as the number of students enrolling in parochial schools has declined, and as the number of seminarians training to become priests has dropped.

One neighborhood church, Our Lady of Pity, a baroque structure with lofty stained glass windows that sits along the route taken by John Paul, has been closed. St. Rita’s, a much humbler building where fresh flowers are the main decoration, won a last-minute reprieve after the Archdiocese considered closing it last year.

Even so, Rev. Gutierrez and many of his parishioners say they are no longer worried about losing their church. The congregation appears to be growing in leaps and bounds.

Italian and Irish immigrants founded St. Rita’s more than half a century ago, and in the past few decades the membership has become mostly Hispanic as immigrants have filled the bleak South Bronx neighborhoods surrounding it. Now, the area is about two-thirds Hispanic.

The transformation has corresponded with a similar change among Catholics on a national level.

A third of American Catholics are now Hispanic, according to the authors of the Pew report. They attribute the infusion of immigrants to the Catholic Church’s continued viability even as other religious denominations have seen their memberships dwindle.

The priests at St. Rita’s recently added two new Masses, and the youth group has swelled to more than 200. Yesterday, more than a dozen mostly elderly congregants showed up for a new noontime Mass dedicated to praying for an end to gun violence and other crime in the neighborhood.

The growth, Rev. Gutierrez says, gives the congregation hope despite its troubles.

“We may be poor, but we are building this church,” Rev. Gutierrez said. “What makes us happy is that we’re growing.”

He added that the proximity of Benedict this week could do even more to reinvigorate the parish. Even if the pope doesn’t come any closer than Yankee Stadium, Rev. Gutierrez said a group of young people from the church is planning to go to Madison Avenue the day before to catch a glimpse of him in the popemobile and wave their banners.

“I think he’s going to see us,” Rev. Gutierrez said.