  We present direct spectroscopic modeling of 44 Type Iax supernovae (SNe Iax)
using spectral synthesis code SYNAPPS. We confirm detections of helium emission
in the early-time spectra of two SNe Iax: SNe 2004cs and 2007J. These He I
features are better fit by a pure-emission Gaussian than by a P-Cygni profile,
indicating that the helium emission originates from the circumstellar
environment rather than the SN ejecta. Based on the modeling of the remaining
42 SNe Iax, we find no obvious helium features in other SN Iax spectra.
However, $\approx 76\%$ of our sample lack sufficiently deep luminosity limits
to detect helium emission with a luminosity of that seen in SNe 2004cs and
2007J. Using the objects with constraining luminosity limits, we calculate that
33% of SNe Iax have detectable helium in their spectra. We examine 11 SNe Iax
with late-time spectra and find no hydrogen or helium emission from swept up
material. For late-time spectra, we calculate typical upper limits of stripped
hydrogen and helium to be $2 \times 10^{-3}$ M$_{\odot}$ and $10^{-2}$
M$_{\odot}$, respectively. While detections of helium in SNe Iax support a
white dwarf-He star binary progenitor system (i.e., a single-degenerate [SD]
channel), non-detections may be explained by variations in the explosion and
ejecta material. The lack of helium in the majority of our sample demonstrates
the complexity of SN Iax progenitor systems and the need for further modeling.
With strong independent evidence indicating that SNe Iax arise from a SD
channel, we caution the common interpretation that the lack of helium or
hydrogen emission at late-time in SN Ia spectra rules out SD progenitor
scenarios for this class.
