  SNe Iax are proposed as one new sub-class of SNe Ia. SNe Iax have been
estimated to account for ~5-30% of the total SN Ia rate, and most SNe Iax have
been discovered in late-type galaxies. In addition, observations constrain the
progenitor systems of some SN Iax progenitors have ages of <80Myr. Recently,
the weak deflagration explosions of Ch-mass CO WDs seem to provide a viable
physical scenario for SNe Iax. Here, comparing theoretical predictions from BPS
calculations with SN Iax observations, we put constraints on the SD Ch-mass
model as a possible Iax progenitor. A long delay times of >3Gyr and low SN
rates of ~3e-5/yr are found in our RG donor channel, indicating that this
channel is unlikely to produce SNe Iax. We predict that the Galactic rate from
the MS (He) donor channel is ~1.5e-3/yr (3e-4/yr), which is consistent with the
observed Iax rate. The short delay times in the He channel support the young
host environments of SNe Iax. However, the relative long delay times in the MS
donor channel are less favourable for the observational constraints on the Iax
progenitor ages. Finally, we set an upper limit on the pre-SN mass-loss rate at
< 10e-4 M_sun/yr (for V_wind=100 km/s). The delay times in the SD Ch-mass model
do not account for that most SNe Iax are located in late-type galaxies.
However, at least one Iax event (SN 2008ge) is hosted by a S0 galaxy with no
signs of star formation. Moreover, current X-ray observations cannot rule out
the SD Ch-mass model. Taking all these into account and considering the
uncertainty of the observed rate for SNe Iax, we suggest that some SNe Iax may
be produced from weak deflagrations of Ch-mass CO WDs in SD progenitors,
especially in the He-star channel. This is consistent with recent analysis of
HST observations for the SN Iax SN2012Z. However, this SD deflagration model is
still unlikely to be the most common progenitor scenario for SNe Iax.
