Why does my basil fall down?

Basil grows best in full sun. It sounds to me like it falls over because the main stem is weak. This is likely due to abnormally long internodes caused by insufficient light. It's called etiolation. If it's growing indoors you can supplement the available light with a "plant Light". Be sure the bulb is a full-spectrum bulb. It needs to contain both red and blue wavelengths of light. If it's growing outside in shade or partial shade move it into full sun. Consider giving it more "root room" -- a 12" pot.