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We study the survival versus disruption of the giant clumps in high-redshift disc galaxies, short-lived (S) versus long-lived (L) clumps and two L sub-types, via analytic modeling tested against simulations. We develop a criterion for clump survival, with or without their gas, based on a predictive survivability parameter $S$. It compares the energy sources by supernova feedback and gravitational contraction to the clump binding energy and losses by outflows and turbulence dissipation. The clump properties are derived from Toomre instability, approaching virial and Jeans equilibrium, and the supernova energy deposit is based on an up-to-date bubble analysis. For moderate feedback levels, we find that L clumps exist with circular velocities $\sim\!50\, km\, s^{-1}$ and masses $\geq\!10^8\, M_\odot$. They are likely in galaxies with circular velocities $\geq \!200\, km\, s^{-1}$, consistent at $z \sim 2$ with the favored stellar mass for discs, $\geq\!10^{9.3}\, M_\odot$. L clumps favor disc gas fractions $\geq\!0.3$, low-mass bulges and redshifts $z\!\sim\! 2$. The likelihood of L clumps is reduced if the feedback is more ejective, e.g., if the supernovae are optimally clustered, if radiative feedback is very strong, if the stellar initial mass function is top-heavy, or if the star-formation-rate efficiency is particularly high. A sub-type of L clumps (LS), which lose their gas in several free-fall times but retain bound stellar components, may be explained by a smaller contraction factor and stronger external gravitational effects, where clump mergers increase the SFR efficiency. The more massive L clumps (LL) retain most of their baryons for tens of free-fall times with a roughly constant star-formation rate.