Scooter stalling on me while running?

I just bought a 1985 Honda Elite 150 Deluxe. I fell in love with it once I took it for a test drive and even drove it 30 miles home. When I rode it the next couple of days it stared acting on me. It stalls on me every time I ride it for a few miles when the gas tank is pretty low, like a quarter of a tank left, but then I noticed once I filled the gas tank again, it runs back into the beast it was when I first rode it. So I was wondering if there's anything wrong with this that I need to fix, or should I just keep the gas tank more than a quarter of a tank at all times?

That means you have to take the fuel tank off and clean it out and also install a new fuel filter. Would be a good idea to change out the rubber fuel lines and clean the carburetor out too. It should run great all the time.