FLT CREW OF B737-300 RPT AUTOFLT LNAV FUNCTION DISENGAGED DURING BOACH RNAV SID FROM LAS. ACFT APPEARED TO BE TURNING TO A HDG IN THE OPPOSITE DIRECTION OF THE SID TRACK. MANUALLY INTERVENED AND CORRECTED.

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DEPARTING LAS ON THE BOACH 2 RNAV DEP CLBING THROUGH 1200 FT AGL WITH LNAV AND AUTOPLT ENGAGED; THE LNAV DROPPED OFF AND THE AUTOPLT STARTED A R TURN WHERE THE HDG BUG WAS SELECTED. FO WAS FLYING AND I INSTRUCTED HIM TO DISENGAGE AUTOPLT AND TURN BACK ON COURSE. ATC NOTICED OUR TURN AND WE ADVISED HIM OUR LNAV DROPPED OFF AND WE ACCEPTED A L TURN TO RECAPTURE THE DEP. WHILE ESTABLISHED ON CLB I WAS GIVEN A TELEPHONE NUMBER TO CONTACT LAS DEP ASAP. I CONTACTED ATC VIA MY CELL ONCE WE LANDED. I WAS ADVISED BY LAS ATC THAT WE (COMPANY) SEEM TO HAVE A SIGNIFICANT NUMBER OF DEPS DROPPING OFF COURSE AS WE HAD EXPERIENCED. I APOLOGIZED FOR ANY INCONVENIENCE OR DISRUPTION WE MAY HAVE CAUSED. I TOLD HIM I WOULD TAKE THIS UP WITH OUR ACR AND WOULD ALSO BE FILING A RPT. HE WAS FAMILIAR WITH THE RPTS. WHEN TURNING OVER THE ACFT OVER TO THE NEW CREW; I ADVISED THEM OF OUR EVENT AND TO BE COGNIZANT OF THE SAME.SUPPLEMENTAL INFO FROM ACN 691801: AS THE CAPT AND I DEBRIEFED WHAT HAD HAPPENED WE TRIED TO COME TO SOME SORT OF CONCLUSION WHAT HAD HAPPENED. SHE THOUGHT MAYBE THE ACFT WAS FLYING TO WHAT WAS SELECTED ON THE HDG BUG ONCE THE LNAV DISENGAGED. ALTHOUGH A GOOD GUESS; I DON'T BELIEVE WE CAN BE SURE. WE DID NOT SEE IF THE LNAV PUSH TILE WAS DE-ILLUMINATED NOR DID WE SEE THE HSEL PUSH TILE ILLUMINATE WHEN THE LNAV DROPPED OFF. WE ALSO DID NOT LET THE ACFT GO FAR ENOUGH TO SEE IF IT WOULD ROLL OUT ON THE SELECTED HDG.