1998 Honda Civic Ignition

Electrical problem
1998 Honda Civic 4 cyl Automatic 80,000 miles

Whenever my car has about 4 gallons of gas left in the tank, the ignition takes longer to catch. If the tank is full it's fine, but I don't know if this is a characteristic for this car or not, or if it could be a minor problem that potentially could get much worse. As far as I know, the refuel light does not come on (if it works, I bought it third hand and although it was from a dealership there are no records of major work being done to it) and I would like to know how to fix it or how much it would cost to fix. (Since it does take longer for the ignition to catch when the gas is semi low, I'm in the habit of refueling it as soon as it begins to take its time starting-it makes me nervous-, so I'm not sure if the refuel light works.)