Fourteen months after opening with great fanfare, the nation's first private hospital dedicated to the care of AIDS patients closed quietly last week, awash in losses of $8 million.

The closing of the Houston hospital dramatizes not only the high costs of caring for AIDS patients but the lack of insurance coverage for many victims of the fatal disease of the immune system.

The 150-bed hospital, known as the Institute for Immunological Disorders, was owned by American Medical International Inc., one of the nation's largest for-profit hospital chains.

The institute opened in September 1986 with a commitment to absorb the cost of care for any uninsured AIDS patient admitted, but officials vastly underestimated the demand for such care. By last March, treatment of indigent AIDS patients had already used up the $250,000 set aside for such care in the whole first year, and the hospital stopped accepting poor, uninsured patients and laid off 15 percent of its workers.

The cost of treating an AIDS patient varies widely, depending on the severity of the illness and the amount of hospitalization required, but can reach $40,000 a year.

In its early months, the hospital received about 1,000 patient visits a month. Some patients were hospitalized, but most were treated as outpatients, without staying at the hospital overnight.

The hospital was unable to achieve a balance between paying and nonpaying AIDS patients, officials said, because many AIDS patients came to the institute as a last resort after exhausting their health insurance benefits to pay for nonhospital care by private doctors.