ABSTRACT We use numerical simulations to analyse the stellar bar evolution in spinning dark matter (DM) haloes. Previous works have shown the halo spin has a substantial effect on bar evolution and can lead to bar dissolution following the vertical buckling instability. We invoke the DM spin sequence, λ = 0–0.09, and study the effect of DM density along this λ sequence by varying compactness of DM halo. We find that (1) varying DM density has a profound effect on bar evolution along λ sequence. (2) For λ ≳ 0.045, the buckling has been delayed progressively. (3) Stellar bars remain near maximal strength, and their amplitude plateau stage extends over 0.7–5 Gyr, terminating with the buckling. (4) Although stellar bars remain strong during the plateau, their pattern speed and size stay nearly constant. This unusual behaviour of stellar bars follows from highly reduced gravitational torques due to DM bar being aligned with the stellar bar. The orbital analysis shows that delayed buckling results from slow evolution of stellar oscillations along bar major and vertical axes, thus postponing the action of the vertical 2:1 resonance which pumps the rotational energy into vertical motions. (5) Peanut/boxy-shaped bulges form at the beginning of the plateau and grow with time. (6) Finally, strong bars in spinning haloes can avoid fast braking, resolving the long-standing discrepancy between observations and N-body simulations. This behaviour of stellar bars along the λ and DM density sequences reveals a wealth of stellar bar properties which require additional study.