LT 1045 Owner's Manaul. Scroll down to page 27, illustration 23. Note that it says that
some models are non serviceable.
Now here are my thoughts on this. We actually need more information to help troubleshoot your question. Here is why...
1) Do you do any heavy towing such as using a lawn roller?
2) Small hills will hasten wear on these transmissions.
3) Any front blade work done with it?
Those transmissions aren't really meant for such chores as rolling lawns even if the lawns are flat. Same for mowing hills and front blade work, i.e. snow removal doesn't help either.
I heard of one gentleman that used his LT 1045 to roll his lawn and the transmission lasted three years. Fortunately it was covered under warranty.
One must consider some things about these types of lawn tractors. Price.... That engine isn't cheap even if the manufacturer buys thousands of them a year. Blow the engine up and you may be amazed as people have found out that the engine costs more than they paid for the tractor and mower when new. Now figure in the deck spindles, seat, gauges, steering wheel, literally ALL the components and the company has to still be able to sell that unit and make a profit. So, do you really think the transmission is really going to be any different when figuring in the companies bottom dollar?
Three years ago two gentlemen asked me about their eleven year old Craftsman garden tractors and what could be wrong with the hydros. BOTH took immaculate care of the whole unit and both mowed slight inclines. Both said the rest of the tractor was still sound as ever and the only thing wrong was the hydro would slip when warm or going up a slight incline. After doing some research the best answer that I could give them was to "try" a new implement relief spring. It would be a "band aid" fix short term. Long term... purchase a new transmission because everything else n the system was worm out.
As usual.... just my rambling thoughts.