In 2004 I bought an MTD Yard Machine, 20hp, lawn tractor. It would take the numerous grades on my property with ease, but now it has trouble even climbing up a sight grade. The drive belt is original. Is the problem that the drive belt has stretched with age and needs replacing, or is it transmission problems?

Does the engine maintain full rpm, if so then your belt is too loose. Replace it or tighten the tension on the idler pulley

This is a forum with the same problem discussed. Same make, but not identical model to yours, but may be worth reading. And a response to ballenger's question will help others here offer advice.

mtd lawn tractor wont pull hills - Tractors Forum - GardenWeb

Hi,
Considering that belts have a life expectancy of 4 - 5 years, that would be a good place to start.
Peace,
Clarke