The Fairfax County School Board has come up with a plan to cover slightly more than half the $6.9 million in federal aid the county could lose if Congress decides to reduce or eliminate the federal subsidy for educating children of military personnel.

In addition to the $2.5 million set aside by the board last spring to cover possible losses in the impact aid program, the board last week agreed to seek permission from county supervisors to shift more than $1 million from the school's operating budget to cover potential impact aid reductions.

At least some of the money could be used to reduce tuition fees the board has threatened to impose on the parents of 1,520 children living at Fort Belvoir if federal funds fall short of the $6.9 million total, according to John Hess, associate superintendent for financial services. School officials warned, however, that the additional funds will not mean substantial reductions in the tuition charges, estimated to range from $2,600 a year for an elementary student to $16,330 for a severely retarded student.

At the same time the board began looking for additional ways to cover possible losses, the U.S. Defense Department intensified its lobbying efforts to prohibit local school boards from charging tuition to military personnel. Last week, the department sent a proposed bill to House Speaker Thomas P. (Tip) O'Neill that would ban any tuition charges to military families regardless of cuts in federal impact aid. The proposed legislation has yet to find a sponsor.

"The Department of Defense strongly believes that this legislative proposal is necessary to prevent the adverse effects on recruitment and retention of military personnel that imposing tuition charges on military dependents would create," Defense Department attorney William H. Taft IV said in the letter accompanying the proposed bill.

In Fairfax County, more than 16,000 children of military personnel are enrolled in the public schools, including the 1,520 children who live at Fort Belvoir. Of the $6.9 million school officials said they need to educate the county's military children, $2.4 million was reserved for the Fort Belvoir youngsters, with the remaining $4.5 million for children of military personnel who live off-base.

School officials have anticipated that Congress will eliminate at least the $4.5 million for off-base students. Because of that, officials said, much of the $3.5 million in county funds would be used to offset those losses, rather than cover education costs for the Fort Belvoir children.

Early this fall, the Fairfax School Board sent letters to parents of the 1,520 Fort Belvoir students, warning them that they could receive tuition bills late this month, depending on the outcome of Congressional action on impact aid.

The struggle over impact aid began last spring when Congress first began considering changes in the impact aid program. This summer, Congress approved $475 million for the program nationwide, a cut of 37 percent over last year. Lawmakers are under strong pressure from President Reagan to make even further cuts, and Reagan has proposed reducing funding to $353 million.

Congress is expected to take action on the funding proposals later this month