The long-struggling Caritas Carney Hospital eliminated 55 full-time jobs recently. The cuts are part of a plan to keep the Catholic hospital alive in an increasingly competitive health-care market, a hospital spokeswoman said. The Dorchester hospital isn't alone. Although it is part of the sprawling Caritas Christi Health Care consortium, the Carney, like many other community-based hospitals, is struggling for survival. Administrators, secretaries and the people who move bedridden patients from room to room were among the 52 people who were laid off, a Carney spokeswoman said. The hospital also eliminated three vacant nursing jobs. The hospital now employs 860 people. When the Carney first opened, in South Boston in 1863, it was New England's first Catholic hospital. Its first few patients were Civil War soldiers. Recently, about 75 percent of the hospital's patients rely on government-funded health insurance plans, such as Medicaid and Medicare, to pay their hospital bills.