IT HAS ALWAYS been difficult to persuade people to report suspected cases of child abuse and neglect, but more people seem willing to do so these days. Public authorities who encourage people to speak up, however, take on a responsibility to provide the means for conducting thorough investigations of the reports. Here, Virginia seems to be falling behind.

In 1975, Virginia's Department of Social Services was given the responsibility for investigating allegations of abuse against children. One year later, there were 21,045 complaints of various kinds of child abuse statewide. By 1986, the number of complaints that had to be investigated by state social workers had more than doubled to 47,888. The number of confirmed incidents of child sexual abuse increased even more rapidly. In 1976, there were 102 confirmed cases of child sexual abuse. By 1986, there were 1,915 confirmed cases.

As the numbers of complaints and substantiated cases continue to grow, however, there has been no significant corresponding increase in the number of social workers the state has to investigate them. For the past five years, there have been about 150 investigators. Virginia Social Services Commissioner Larry Jackson says his investigators have been able to spend less than six hours on each case.

For the fiscal 1989-90 budget, the Department of Social Services asked for $4.3 million more than Gov. Baliles finally decided to allocate for such investigations. The extra sum would allow the hiring of 61 more social workers, nine supervisors and 14 clerks. It would also increase the amount of time that could be spent on each allegation. But as the state legislature considers the budget, it appears that there will be no funds for more child-abuse investigative services. In a state budget of $22.5 billion, surely a few million dollars can be added to rescue victims of child abuse.