ANOTHER school superintendent has now announced his resignation. This time it's Edward Andrews of Montgomery County. His reasons are typical. He has been worn down by the administrative demands of a large school system, vastly compounded by the erratic behavior of a misguided school board.

For Montgomery County voters, his departure only increases the importance of the school board election in November. That board's first preoccupation will necessarily be to find a replacement for Mr. Andrews before he leaves in June. For two years, he has been the shock absorber between the board and the schools, representing decency and stability in a period of Montgomery school politics when both commodities were in short supply.

But Mr. Andrews' departure fits so clearly into a wider pattern that it ought not to be treated as more Montgomery politicking. It's necessary to ask whether school boards, and the public in general, have not defined a superintendent's job in terms that are impossible to fulfill.

Of the six big school systems in Washington and its closest surburbs, one has a superintendent -- Edward Feeney of Prince George's -- who has been in the job for six years. All of the other five have taken office since the beginning of 1980. Running a big urban school system is like hunting tigers with a slingshot; it offers moments of excitement, but, as a career, it doesn't promise long tenure.

You could argue that a school superintendent is a public official of great influence, and ought to be subject to removal. But the same rule presumably applies to elected officials, and superintendents in this area seem to turn over much faster than mayors and county executives, not to mention U.S. senators. Sometimes superintendents leave at their own initiative, like Mr. Andrews or Vincent Reed, who resigned as Washington's superintendent in 1980. Sometimes they are pushed out by their boards, like Lynton Deck in Fairfax County this year, and Larry Cuban in Arlington last year. But it is simply wrong to claim, as school boards sometimes are tempted to do, that this custom of irregular terms and early departures makes the schools responsive to boards' policy. On the contrary, the long wrangles between board and superintendent, followed by the long search for a successor, are usually enormously disruptive to the schools.

Why does it happen? The essential answer is that over the past generation the great issues of public morality and ideology have increasingly gravitated toward the schools. While Congress can refuse to deal with the implications of busing or of standardized testing, the schools cannot. But that isn't likely to change very soon. It's time for school boards, and not only in Montgomery County, to give careful thought to the way they have been using their superintendents, and using them up. The present practice runs through too many good people too fast, with too little benefit to schools and schoolchildren.