Small Engine Troubleshooting Problems? Ask a Mechanic Now.
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My first thought is that you most likely have a belt that is slipping once it gets warm. Have you replaced the transmission drive belt recently on the machine? This is the first place I would look at.
Did you replace it with an original equipment belt or an aftermarket belt?
If the belt were routed wrong it would not likely work at all. Give me a moment to take a look at some information about your machine.
The only other thing that you could have is a hydro pump going bad, it gets weak once it gets warm.
Your transmission does have an internal filter in it that could be getting stopped up after running a little while. The only way to get to it however is to remove the transmission from the machine and disassemble the transmission. The filter is inside the transmission. It does not appear that Snapper supplies the part therefore you would have to go back to the transmission manufacture(Tuff Torq) in order to get a replacement filter.