What was found
AUTOPILOT "A" WOULD NOT REMAIN ENGAGED 3 ATTEMPTS. GROUNDED-YES. REMOVED "A" AUTOPILOT AILERON ACTUATOR, PER B737-900 AMM 22-11-25-000-801. PERFORMED AUTOPILOT AILERON ACTUATOR LINKAGE INSPECTION, PER AMM 22-11-25-200-801, WITH NO DEFECTS NOTED. INSTALLED "A" AUTOPILOT ACTUATOR, PER AMM 22-11-25-400-801. REMOVED AND REPLACED AILERON POSITION SENSOR, PER AMM 22-11-29-000-801/AMM 22-11-29-400-801. ADJUSTMENT AND TEST CHECKS GOOD. ACCOMPLISHED AMM TASK 22-11-29-400-801 STEP G (1) LLM MAINTENANCE TEST AILERON POSITION SENSOR TEST, TEST GOOD. ACCOMPLISHED AMM 22-11-25-400-801 STEP I(1) (A)1) LLM MAINTENANCE TEST FOR AUTOPILOT AILERON ACTUATOR, TEST PASSED. NO FAULTS FOUND. GROUND VERIFICATION ACCOMPLISHED.