The always on orbit exists and is called a dawn-dusk Sun synchronous orbit. It is an orbit that is always above the terminator (line between night and day) where it can face the Sun 100% of the time.

This orbit has to rotate about a degree every day to follow the terminator as the earth orbits the Sun. It uses the equatorial bulge of the earth to achieve that rotation without have to spend rocket fuel. It is really quite interesting.