What was found
WHILE IN CRUISE AT FL340, AUTOPILOT B DISCONNECTED, COMPLIED WITH QRH, WOULD NOT STAY ENGAGED, TRIED AUTOPILOT A AND IT DISCONNECTED AS WELL, AND WOULD NOT STAY ENGAGED. THEN NEITHER AUTO PILOT WOULD ENGAGE AT ALL. NO OTHER ANORMALIES, NO CIRCUIT BREAKERS POPPED. FLIGHT DIRECTORS AND AUTO THROTTLES WORKED NORMALLY. GROUNDED - YES. INITIAL T/S FOUND MAINT MSG 22-11176 STAB TRIM MAIN ELEC FAULT, REF B737-800 FIM 22-13 TASK 818, REMOVED AND REPLACED MAIN ELEC STAB TRIM RELAY, R64, PERFORMED REPAIR CONFIRMATION REF B737-800 AMM 22-11-00-740-806, RUN SELECT LIBRARY TEST SPEED/STAB TRIM 32 PASSED. PERFORMED LAND VERIFY SUCCESSFUL REF AMM 22-11-00, AUTOPILOT A+B OK FOR SERVICE, CABIN PRESSURE LEAK TEST SUCCESSFUL.