We study the bases and frames of reproducing kernels in the model subspaces K_⊖ ² = H² ⊖H² of the Hardy class H2 in the upper half-plane. The main problem under consideration is the stability of a basis of reproducing kernels k_λn (z) = (1-⊖(λ_n)⊖(z))/(z - λ_n) under "small" perturbations of the points λ_n. We propose an approach to this problem based on the rerently obtained estimates of derivatives in the spaces K_⊖ ² and produce estimates of admissible perturbations generalizing certain results of W.S. Cohn and E. Fricain.