The nature of the progenitors and explosion mechanism of Type Iax supernovae (SNe Iax) remain a mystery. The single-degenerate (SD) systems that involve the incomplete pure deflagration explosions of near-Chandrasekhar-mass white dwarfs (WDs) have recently been proposed for producing SNe Iax in which non-degenerate companions are expected to survive from SN explosions. In this work, we concentrate on the main-sequence (MS) donor SD progenitor systems. By mapping the computed companion models from three-dimensional hydrodynamical simulations of ejecta-companion interaction into a one-dimensional stellar evolution code MESA, we investigate the long-term appearance and observational signatures of survivingMS companions of SNe Iax by tracing their post-impact evolution. Depending on different MS companion models, it is found that the shocked surviving companion stars can significantly expand and evolve to be more luminous (5-500L(circle dot)) for a time-scale of 10-10(4) yr. Comparing with the late-time light curve of an observed SN Iax (SN 2005hk), it is suggested that surviving MS companions of SNe Iax would expect to be visible about 1000 d after the explosion when SN itself has been faded.