The Senate failed for the second time yesterday to cut off a liberal filibuster against a provision to restrict busing of students for desegregation purposes.

The 54-to-32 vote to limit debate fell six short of the number required. Had all absentees voted it appeared that the anti-busing forces would have had almost exactly the 60 votes needed. But now the Justice Department authorization bill to which sponsors sought to attach the anti-busing language will be set aside Wednesday so the Senate can take up the tax-cut bill. The Senate may not return to the busing issue until after the August recess.

Last Friday some busing opponents voted against a first cloture motion because it would have resulted in striking down part of their amendment as non-germane. But yesterday's vote probably accurately reflected the Senate's feeling on forced busing.

Had cloture succeded, debate would have been limited to 100 hours on an amendment by Sen J. Bennett Johnston (D-La.) forbidding federal courts to order students bused more than five miles or 15 minutes from their homes.

Yesterday was the 12th day that the Senate has devoted part of its time to the bill setting spending ceilings for Justice Department activities next year. For much of that time Sen. Lowell P. Weicker Jr. (R-Conn.) has held the floor conducting a filibuster to prevent a vote on amendments by Sen. Jesse Helms (R-N.C.) forbidding the department to become involved in busing suits and then Johnston's amendment which seeks to limit the authority of the courts.

If Johnston ever is able to get his amendment to a vote he appears certain of getting a majority, which is all he needs to pass it. But liberals could then mount a second filibuster against the parent Helms amendment and a third against the bill itself. Some lawyers believe both amendments are unconstitutional.