We model and analyse the secular evolution of stellar bars in spinning dark matter (DM) haloes with the cosmological spin lambda ~ 0 -- 0.09. Using high-resolution stellar and DM numerical simulations, we focus on angular momentum exchange between stellar discs and DM haloes of various axisymmetric shapes --- spherical, oblate and prolate. We find that stellar bars experience a diverse evolution which is guided by the ability of parent haloes to absorb angular momentum lost by the disc through the action of gravitational torques, resonant and non-resonant. We confirm the previous claim that dynamical bar instability is accelerated via resonant angular momentum transfer to the halo. Our main findings relate to the long-term, secular evolution of disc-halo systems: with an increasing lambda, bars experience less growth and dissolve after they pass through the vertical buckling instability. Specifically, with an increasing halo spin, (1) The vertical buckling instability in stellar bars colludes with inability of the inner halo to absorb angular momentum --- this emerges as the main factor weakening or destroying bars in spinning haloes; (2) Bars lose progressively less angular momentum, and their pattern speeds level off; (3) Bars are smaller, and for lambda >= 0.06 cease their growth completely following buckling; (4) Bars in lambda > 0.03 haloes have ratio of corotation-to-bar radii, R_CR / R_b > 2, and represent so-called slow bars which do not show offset dust lanes. We provide a quantitative analysis of angular momentum transfer in disc-halo systems, and explain the reasons for absence of growth in fast spinning haloes and its observational corollaries. We conclude that stellar bar evolution is substantially more complex than anticipated, and bars are not as resilient as has been considered so far.
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