What characteristic prevents stars like the Sun from continuing to fuse elements heavier than carbon or oxygen?

Answer

They lack the gravitational power to heat their cores sufficiently to fuse carbon.

Stars less massive than about eight times the Sun cannot generate the extreme core temperatures and pressures needed to ignite subsequent fuels like carbon, causing them to contract into a white dwarf instead.

What characteristic prevents stars like the Sun from continuing to fuse elements heavier than carbon or oxygen?
Elementastronomystarmassnucleosynthesis