Is there an upper limit to the mass of a star above which it would not enter the AGB? If so, why?
AGB stars have a mass less than about 10 solar masses.
AGB stars evolve from red giant stars. A red giant forms when a star runs out of hydrogen and undergoes core collapse until the core is hot enough to start helium fusion.
Stars over 10 solar masses start helium fusion as the hydrogen supply becomes exhausted. They progress through fusing heavier and heavier elements until they have an iron core. This then collapses and a supernova explosion occurs.