Under FAR Part 121, is it mandatory to execute a missed approach when unable to land within the touchdown zone?
This is spelled out in 91.175(c), in particular


  Operation below DA/DH or MDA. Except as provided in paragraph (l) of this section or § 91.176 of this chapter, where a DA/DH or MDA is applicable, no pilot may operate an aircraft, except a military aircraft of the United States, below the authorized MDA or continue an approach below the authorized DA/DH unless


...


  The aircraft is continuously in a position from which a descent to a landing on the intended runway can be made at a normal rate of descent using normal maneuvers, and for operations conducted under part 121 or part 135 unless that descent rate will allow touchdown to occur within the touchdown zone of the runway of intended landing