While defective bulbs cause issues with lighting, certain fixtures also require different bulbs. For multilight fixtures, the heat inside the fixture creates a problem for the bulbs. You need a lower wattage bulb that emits less heat to light the fixture properly. Check that your burnt out bulb is the same wattage as the others in the fixture.
If you recently installed the wiring for the multilight fixture, then the wires may not work well with the type of light fixture, particularly if you need multiple bulb points. The wiring also might be corrupted in the light fixture itself for the connection that holds your single burnt out bulb. If you have an antique lighting fixture, then you need to open the fixture and look for rust or split wires inside where the bulb connects. You can always replace the wiring or hire a professional electrician.
To check your house's voltage, purchase a multimeter at an electronics store. Test a wall outlet with the multimeter's probes. If uncomfortable testing the wall outlet, then ask an electrician to diagnose the voltage in your home. If you find a voltage over 125, then call your power company. Your multilight fixture is receiving too much energy, so one bulb burning out may eventually lead to others burning out.
If you notice flickering in the single light bulb before burning, then the connection either in the fixture or the wires is off. As the bulb flickers on and off, you wear down the bulb's life. Flickering also leads to fires, as the bulb gets overly hot, particularly if you have multiple bulbs plugged into one connection. If you notice flickering, turn the power off to the connection through the breaker box and remove the light fixture. Check that the bulb is tightly screwed into the fixture and that the connection is not loose once you screw in the bulb.