Why is 128-bit considered "medium term" security? Why is 128-bit encryption considered good enough for medium term security only?  How is expected to be eventually broken?  Quantum computing or brute force attack?
Why is 128-bit encryption considered good enough for medium term
  security only?


Because in the long term it is expected that mankind will be able to carry out $2^{128}$ operations because it's not physically as impossible as $2^{256}$ operations.


  Quantum computing or brute force attack?


Assuming quantum computers work at a speed comparable to classical computers nowadays, they can break 128-bit encryption using $2^{64}$ operations (Grover's algorithm) which is considered feasible in the long-term, of course this should be considered additional to classical brute-force which may also be feasible at some point.