I need some help solving an issue i have been having with my 01 honda Rubicon Foreman 500 (TRX500FA1).

my bike runs normal starts up and drives great with lite use, but for some reason when i am in 2nd gear or higher if i accelerate to quickly it sputters and backfires then dies, i don't know if it has something to do with the rpm it is at or what but it seems to do it in higher rpm while its in gear, i doesn't die when in high rpm in neutral.

when it dies is just seems like its not getting fuel and sometimes makes a little pop backfire but it wont recover from giving it throttle while it dies it just dies.

Now there is a few things to note: i have rebuilt the carb 100% tear down soak replace etc..
I checked the fuel cap " air flows through it but i'm not sure how freely it should pass through i feel as it is a bit hard to blow through it but air does flow through " I'm wondering if it has something to do with the fule cap ventilation but i have no idea?????

i gave it a oil change, changed the sparkplug blah blah blah. pretty much a basic tuneup.

i am completely stumped as to of what could be wrong with it, when it is in neutral i can literally open throttle up all the way and hold it open and it does not die.
does anyone have any idea of what could possibly be going on?