It would seem strange to me that a dirty airbox would cause the problem you're having. I'd think the air filter would have to be completely caked with dirt to cause the stalling problem you're having. And if that were the case it, cleaning the carb wouldn't help. A clean, oiled air filter will clean the incoming air just fine. If you're riding where it's extremely dusty, you can add a pre-filter.

When you notice the bike start to lose power, shut the bike off and open the fuel tank. If you get a whoosh of air, the tank vent isn't working and you're slowly pulling a vacuum on the tank which is starving the engine of fuel.

You might also check the breather hose from the crankcase to the airbox. If it's blocked, you could be building up crankcase pressure while riding.