IDIOMS

lost cause

(idiomatic) A cause, attempt, or effort that is hopeless or futile.

Example:   He has already made up his mind, and it's a lost cause to try to change it.
2015, Paul Wilson, Alexis Sánchez sends Arsenal into final after gallant Reading go the distance (in The Guardian, 18 April 2015)[1]
  Artfully pulling the ball back to leave McCleary chasing a lost cause, Sánchez calmly made space for a shot and applied a finish that beat the despairing dives of both Federici and Michael Hector, the latter vainly attempting to recover position when it was too late.