  In this paper, we investigate the validity of the so-called cosmic no-hair
conjecture in the framework of anisotropic inflation models of non-canonical
scalar fields non-minimally coupled to a two-form field. In particular, we
focus on two typical {\it k}-inflation and Dirac-Born-Infeld inflation models,
in which we find a set of exact anisotropic power-law inflationary solutions.
Interestingly, these solutions are shown to be stable and attractive during an
inflationary phase using the dynamical system analysis. The obtained results
indicate that the non-minimal coupling between the scalar and two-form fields
acts as a non-trivial source of generating stable spatial anisotropies during
the inflationary phase and therefore violates the prediction of the cosmic
no-hair conjecture, even when the scalar field is of non-canonical forms. In
connection with the Planck 2018 data, tensor-to-scalar ratios of these
anisotropic solutions are investigated. As a result, it appears that the
tensor-to-scalar ratio of the anisotropic power-law inflationary solution of
{\it k}-inflation model turns out to be more highly consistent with the Planck
2018 data than that of Dirac-Born-Infeld model.
