2007 LA165 Stops Moving After 30 Minutes Of Mowing

This is my first half-season with a 2007 LA165 24up Briggs and Stratton 48 inch mower deck that I bought used with about 300 hours on it from a local John Deere dealer. I mow about a 1/3 of an acre that is relatively flat but does have a short 45 degree slope at the back of the yard. Now I'm not a small guy at 6'3 and about 380lbs. What I'm experiencing is that after about a half hour of mowing the mower slows down until it stops moving. I do not notice any problems with the engine and the mower deck. This problem has happened once before and the problem went away for a bit after I changed the belts. With a hydrostatic transmission I keep my foot on the forward pedal and I do not use the cruise. I was angry when it happened so I just waited for the mower to cool off a bit and then parked it in the garage and walked away. I'm somewhat handy so when I get around to fixing this thing what are some of the causes that I should be looking for? Any help would be most appreciated. Thanks.

If the tranny growls when you use it then chances are it is on it's way out.
A bit dissapointing to get one like that from a dealer.
JD use light oil in their hydros so usually you can tease some more life out of one by changing to a heavier grade oil ( 20W 50 ) if & only if you do not use it in the snow.
The L series trannies usually start going in the 400-500 hour mark and an oil change can squeeze another 100 to 200 hours out of them.
Make sure that the case is clean so the oil can cool & check that the fan is working, they can strip so not actually pump.
And on that subject, the pulley is on a fine spline & they have been known to strip as well.
However this is generally indifferent to time.

So start by having a word to the shop you bought it from.
If they recommend replacement, then go to Mulligans, not them.
There is a pump/motor ( called core ) replacement kit available but you need a very clean enviroment to do this work.
I use the workshop bathroom after spraying the walls with water & keep the tranny covered with a damp shop towel when not working on it.
Disposable painters coveralls & hat.
Trannise get remover, pressure washed, soda blasted then hot watr washed before I even think of opening them up.

I don't remember hearing the transmission growl. The engine was on a faster idle and the cutting looked fine. I'll call the shop tomorrow and see what they say. After that I guess I will need to find out what transmission I have. Yeah, it sucks. That's why I went to a dealer in the first place.

Got the same issue with a LA120 with a T-40 hydro, fortunately they can be rebuilt lots of youtube videos, hopefully its not to hard. I heard about 20w50, what should one do after a rebuild add 20w50 or is there something on a rebuild

I am yet to see one single how to video on rebuilding hudros dom=ne by a person who actually know what they are blathering about.
I see people doing them without properly washing the outside of the case, others working on dirty floors or benches.
I try to avoid pulling one down but when I do it id done in the bathroom after hosing the walls & floor down.
The box gets covered with a damp lint free shop tow any time my hands are not inside it.
Before the box gets split, it is blown down , degreased, pressure washed , soda blasted & rinsed.
In videos I see dirty greasy boxes getting split and bloke shoving tools inside with globs of gunk on them.
When fixed like that they won't stay fixed for very long.