THE CAPTAIN OBTAINED NO RESPONSE TO NOSE-UP STABILIZER TRIM DURING DESCENT. NORMAL NOSE-DOWN TRIM REMAINED OPERABLE; ALTERNATE TRIM WAS NOT ATTEMPTED. THE CREW REPORTED A JAMMED STABILIZER AND LANDED WITH NOSE-DOWN TRIM. DISASSEMBLY OF THE HORIZONTAL STABILIZER CONTROL UNIT SHOWED INADEQUATE LUBRICANT AND EXTENSIVE CORROSION IN A GEARBOX. THE AIRFRAME MANUFACTURER'S PROCEDURE FOR REPLENISHING THE GEARBOX LUBRICANT COULD RESULT IN UNDERSERVICING. THE OPERATOR OBSERVED A GEARBOX SERVICE INTERVAL WHICH WAS 250% OF THE MANUFACTURER'S RECOMMENDATION.