Yes, it is quite possible. There are a lot of stories out there about the K46 transmission that is in your tractor. But I have the same transmission and mine is 7 years old and still going strong.
You can try to change to change the oil in the transaxle and filling it with synthetic oil, but seeing it is a sealed unit, it's not real easy. But the inability to climb hills when it is warm is the first sign of failure.
