Kind of a shot in the dark, but-
Check the governor linkage and carb throttle shaft for binding when the problem occurs.

Thanks, Bill. Your suggestion makes a lot of sense. Follow up questions for you: how do I know if there is binding going on? Tonight I pulled the plate out that covered the muffler and there was the throttle and choke cable going into what I am assuming was the carberator. I checked both cables with the engine on and off. If anything, there was a bit of slop in both from use. Not bad, just from wear I would guess.

If the PTO clutch is the type that has a "blade brake" function built into it, it's possible that the PTO brake is dragging hard.

You would have to disconnect the throttle cable to the carb, but if you are ASSUMING a part is the carb, I'm not sure you should be taking anything apart.
Not trying to be mean, but It's hard to describe how to put stuff back together from the keyboard.

Float valve

First, take the mower drive belt off the PTO and make sure all the pulley shafts on the deck turn smooth and spin free. If any are binding that can be your problem. If not, then you've eliminated the mowing deck.

Some JD PTOs have a gap adjustment. If your X304 does that could be the problem.

Could also be a marginal battery. Remove the battery, take it to Autozone and have it load tested.

Has this issue been solved? If so what was it? My x304 is doing the exact same thing! Help

I like justalurkers advice about checking the spindles for binding. Maybe after some use, the bearings are getting hot and "partially" seizing. Not bad enough to really notice when the engine is up to speed and producing full power, but enough when the engine is at low speed and producing much less power.

I would love to here from Pflemming. I would like to know if he fixed it and what the problem was. So far I called the dealer and they said it could be the battery or the coil packs that are getting weak when the engine gets warm or the carb could need cleaning. I brought the battery to autozone and had it tested. They said it is fine. None of the belts are worn and all spindles turn freely. I also checked the gas cap vent it was clogged but it didn't solve the issue. It has 70hrs on it.

Have you removed the deck drive belt from the PTO? If yes, does the motor still die when it's hot with the deck drive belt off? If no, then remove the belt and see if the motor dies.

Try new plugs correctly gapped.

I've seen coils lose spark when hot. EZ to check... use insulated pliers to remove one plug wire when it's running funny. If it dies then that side is working. Try the other plug wire. If it stays running then you found the side the problem is on. either coil, wire, or plug.

Just for info - I did a search on "Pflemming88" and he only made the one post in 2012. Nothing before or after.

Thanks Tom for your time.

Thanks lurker! I have not tried pulling the belt off the pto and engaging the pto to see if it bogged down. But it is a great idea! Also very good advise on the coil issue. I will try this as soon as I get a chance. I am going on vacation this weekend and won't be back for a week so I will get back to you guys as soon as I can.

Thank you all for your help!

Sorry it's been so long but I think I found the problem! Thanks to all you guys! I had my wife sit on the tractor and turn on the blades. While it was bogging down I pulled the right side coil wire and the tractor died. I then started it up again and once again engaged the pto and while it bogged I pulled the left coil wire and the tractor did not run any different. So the issue must be the left side coil. Does anyone know how to change it? Or the part #'s I need?

Thanks guys

May not be the coil. Could be a bad plug, plug wire, or bad connection on a smaller wire.

Check the easy, simple, and cost effective things FIRST.

I will try a plug at the end of the week when I mow again. Isn't it kind of strange it only happens when it's hot?

The symptoms are the symptoms... an orderly and systematic diagnostic procedure is the way to do it.

Would you be happier if you bought a coil and then found out you had a bad plug cap, plug wire, plug, or just an iffy low voltage connection or a bad ground?

You might not be losing spark when it's hot you could be losing compression. You need to KNOW that you're losing spark when hot cause a tight valve could manifest the same symptoms.

Coils do fail on these at times. The cover is easy to remove and is slotted if I recall. As JL noted, it could be a plug. Ideally, if it does it and you can quickly pull the cover, remove the small kill wire at the affected side coil and do a recheck. You don't want to run this for more than a minute w/o the cover on. And keep your fingers outta the flywheel ....