Did the bike sit for a long while with gas in it?
What happens over time is the gas starts to break down (go bad).
When it does this, it turns into almost a varnish.
This starts plugging the holes in the jets, and the ports drilled in the carb, starting with the smallest, which is the idle circuit.
What is happening in your case is when you spray carb cleaner down the carb, it starts and runs on that, until it's used up.
You need to remove the carb and "boil it out" (clean and rebuild), paying attention to the idle jets and ports.
This diagram of the carb might help you:
http://www.bikebandit.com/houseofmotorcycles/2005-yamaha-yz85-yz85t-carburetor/o/m145327sch299511
Again, pay attention to the idle jet (pilot jet), #8 in the diagram, inside the float bowl.
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