Unfaltering means unwavering, not changing. As an adult, you might thank your mother for her unfaltering support of your education, never letting you skip a night of homework. Now, not so much.
To falter means to almost lose strength or momentum, but not necessarily lose it entirely. If you are standing at the entrance to the stage, and thinking "I just can't go out and make a speech," you're faltering. If you never have that moment of doubt, your desire to give the speech could be described as unfaltering.