Abstract We predict, analytically and by simulations, that gas discs tend to survive only in haloes above a threshold mass ∼2 × 1011M⊙ (stellar mass ∼109M⊙), with only a weak redshift dependence. At lower masses, the disc spins typically flip in less than an orbital time due to mergers associated with a change in the pattern of the feeding cosmic-web streams. This threshold arises from the halo merger rate when accounting for the mass dependence of the ratio of galactic baryons and halo mass. Above the threshold, wet compactions lead to massive central nuggets that allow the longevity of extended clumpy gas rings. Supernova feedback has a major role in disrupting discs below the critical mass, by driving the stellar-to-halo mass ratio that affects the merger rate, by stirring up turbulence and suppressing high-angular-momentum gas supply, and by confining major compactions to the critical mass. Our predictions seem consistent with current observed fractions of gas discs, to be explored by future observations that will resolve galaxies below 109M⊙ at high redshifts, e.g. by JWST.