B737-700 CREW HAD HDG DEV IN MMEX CLASS B AIRSPACE.

Narrative

ACFT DID NOT FOLLOW HDG COMMANDS AND PLTS FAILED TO CATCH THE ERROR. APCH ENTERED IN FMC IN ACCORDANCE COMMERCIAL CHART FOR MEX; BUT WAS BEING VECTORED AT 300 KTS BY APCH AND MANEUVERING TO AVOID TSTMS IN VICINITY OF PCA AND SMO VORS. APCH CLRED US DIRECT TO SMO; OPERATING IN AUTOPLT A WITH HDG SELECT; VERT SPD; MCP SPD ENGAGED. TURNED HDG TO SMO USING FORWARD VISUAL DISPLAY. MOVED SMO TO #1 ON CDU AND EXECUTED. I THEN BECAME ENGAGED IN ATTEMPTING TO GET BACK ON APCH PROFILE BY SMO AND NEGLECTED TO XCHK THAT ACFT WAS PERFORMING AS COMMANDED -- IT WAS NOT. APCH RECLRED DIRECT SMO. WE THEN ENCOUNTERED MODERATE FREEZING PRECIP -- NOT PAINTING ON RADAR -- AND LIGHT TO MODERATE TURB. AT SOME POINT; I REALIZED THE ACFT WAS NOT OBEYING HDG COMMANDS; DISENGAGED HDG AND RE-ENGAGED SUCCESSFULLY. APCHING SMO; WAS GIVEN A HDG BY APCH TO REINTERCEPT S OF SMO. ACFT AGAIN DID NOT FOLLOW HDG COMMAND. DISCONNECTED AUTOPLT AND FLEW MANUALLY. MADE LOGBOOK ENTRY. DID NOT OBSERVE CTL WHEEL STEERING OR HDG DISENGAGEMENT. MIGHT HAVE FLOWN NEAR TERRAIN IN VICINITY OF MEX WERE IT NOT FOR MEX APCH CTL AND EVENTUAL VISUAL CONDITIONS. I DID NOT OBSERVE ACFT DEVIATING FROM MCP COMMANDS. FO DID NOT CATCH EVENTS. HIGH WORKLOAD ENVIRONMENT. THIS EVENT IS UNUSUAL; IN THAT I AM STILL NOT SURE WHETHER WE FAILED TO OBSERVE A WARNING THAT THE HDG SELECT FEATURE DISCONNECTED; OR IF IT WAS A MECHANICAL PROB. IF THE EVENT WAS A MECHANICAL FAILURE; I HAVE NOT SEEN IT BEFORE AND IT WOULD BE A VERY UNUSUAL EVENT. IF; HOWEVER; IT WAS A WARNING MISSED BY THE CREW; PREVENTIVE ACTION WOULD BE INCREASED SCAN BY BOTH. IT WOULD HAVE BEEN DIFFICULT TO DECREASE WORKLOAD IN THIS CASE.