In the TC29, your transmissions and rear axle lubricant and hydraulic fluid are one in the same...all 37 gallons of it. The filter is on the right hand side, approx. under the seat. You will see it if you look between the right rear tire and the rear axle inside the fender. The dipstick for this is under/behind the seat-sort of under the left hand corner, check the oil level....BUT....if the tractor had been sitting for long periods without use, you can get a lot of moisture from condensation inside the axle/transmission. Quarts to gallons worth over time. Especially if the tractor had been stored outdoors without cover. I have experienced this.
The water separates from the oil and sits in the bottom of the axle/transmission case when the tractor is sitting. Once you use the tractor, the water and oil churn together. This could be your issue.
When you shut the tractor off, the water and oil separate again and operation returns to normal.
Changing the oil and filter might remedy your issue. I got my filter at the local NAPA dealer and my local WalMart stocked the transmission/axle oil in 5 gal containers...My tractor took 7 1/2 jugs. Easier than changing oil in your car because no jack needed.
When this happened to me, it also started blowing out o-rings in my hydraulic couplers.
Just my experience, your mileage may vary...as they say.
