MLG ON VECTOR FOR VISUAL APCH TO RWY 25R WAS KEPT TOO HIGH TWICE FOR VISUAL APCHS TO ARPT. ON THIRD APCH ACFT WAS ABLE TO LAND. CTLR TRAINING IN PROGRESS.

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WE WERE APCHING LAX FROM N ON FILLMORE 4 PROFILE DSCNT. APCHING SMO VOR WE WERE TOLD TO EXPECT VISUAL APCH TO RWY 24R. WE WERE THEN CLRED TO 5000' AND THEN LATER REDUCED TO 180 KIAS. AFTER WE XED SMO VOR WE WERE TURNED TO 160 DEG HDG INSIDE OF THE PUBLISHED VISUAL FLT TRACK; BUT WERE NOT GIVEN A LOWER ALT OR A REDUCED AIRSPD. ON THE 160 DEG HDG WHEN ABEAM THE END OF RWY 24R WE WERE CLRED FOR VISUAL TO RWY 25R; BUT TO STAY TO RIGHT OF AN INBND WDB BELOW AND TO OUR LEFT. THE WDB WAS USING RWY 25L. AT THIS POINT I WAS AT 5000'/180 KIAS; 4.5 NM FROM END OF RWY 25R. AN IMPOSSIBLE SITUATION. WE ATTEMPTED THE APCH AND WENT MISSED APCH AT 1000' OVER THE END OF RWY 25R. ON THE NEXT APCH LAX TRACON VECTORED US BACK TO SMO VOR FOR THE SAME VISUAL APCH. TO MAKE A LONG STORY SHORT; WE WERE PUT BACK INTO THE EXACT SAME SITUATION--5000' AND 4.5 MI FROM END OF RWY; HIGH AND WITH TFC BELOW LEFT. AGAIN WE ATTEMPTED APCH AND WENT AROUND AT 500'. ON THIRD APCH WE WERE GIVEN 10 MI FINAL AND REASONABLE ALT. WITH RWY 24L CLOSED LAX TRACON IS TRYING TO PUT 6 LBS INTO A 5 LB BAG. THEY ARE PUSHING THE SYS PAST REASONABLE LIMITS AND PUTTING ACFT AND CREW IN IMPOSSIBLE SITUATIONS. A PHONE CALL TO THE MGR ON DUTY AT LAX TRACON BROUGHT THE EXPLANATION THAT WE WERE BEING HANDLED BY A TRNEE CTLR ON THE FIRST 2 APCHES WHO KEPT US TOO CLOSE TO THE ARPT AND FORGOT TO DSND US ON THE TURN TO BASE LEG. I UNDERSTAND THEIR DILEMMA WITH RWY 24R CLOSED; BUT THEY SIMPLY CANNOT FORCE THE SYS PAST ITS OR ACFT OPERATING LIMITS.