Let's get a little more info... What size jets (main in particular; it sounds like the pilot is OK) are you currently running? I see you've got the TORS delete kit for the carburetor, so I'm assuming you're running the stock carb?
Here's a couple really odd things you may wanna check. One, be sure that your exhaust is not plugged up, either with carbon, a mouse nest, maybe a plug you forgot to remove from the last time you washed the quad?
Two, check your float level inside the carburetor, and set it to 20-21mm. If the float is too high, the engine won't recieve enough fuel when the main jet comes online, and it will fall flat on its face.
Three, remove and clean your fuel petcock. A clogged or restricted petcock will give you the same problem as a mis-adjusted float. Pull the fuel line off the carb, turn the gas on, and you should have a steady stream of fuel out of the petcock. A thin 'ribbon' of fuel, a trickle, or nothing indicates blockage or restriction.
Also, put an inline spark tester on the engine, run it, and watch for fire while you rev it. Your problem sounds fuel-related, but do the spark test to be sure that you're not losing fire when the engine dies out.
Does the engine rev OK with no load on it, and just die out when under a load? Or will it not rev without bogging, even with the trans in neutral and it just sitting there?