  Nebular HeII emission implies the presence of energetic photons (E$\ge$54
eV). Despite the great deal of effort dedicated to understanding HeII
ionization, its origin has remained mysterious, particularly in metal-deficient
star-forming (SF) galaxies. Unfolding HeII-emitting, metal-poor starbursts at z
~ 0 can yield insight into the powerful ionization processes occurring in the
primordial universe. Here we present a new study on the effects that X-ray
sources have on the HeII ionization in the extremely metal-poor galaxy IZw18 (Z
~ 3 % Zsolar), whose X-ray emission is dominated by a single high-mass X-ray
binary (HMXB). This study uses optical integral field spectroscopy, archival
Hubble Space Telescope observations, and all of the X-ray data sets publicly
available for IZw18. We investigate the time-variability of the IZw18 HMXB for
the first time; its emission shows small variations on timescales from days to
decades. The best-fit models for the HMXB X-ray spectra cannot reproduce the
observed HeII ionization budget of IZw18, nor can recent photoionization models
that combine the spectra of both very low metallicity massive stars and the
emission from HMXB. We also find that the IZw18 HMXB and the HeII-emission peak
are spatially displaced at a projected distance of $\simeq$ 200 pc. These
results reduce the relevance of X-ray photons as the dominant HeII ionizing
mode in IZw18, which leaves uncertain what process is responsible for the bulk
of its HeII ionization. This is in line with recent work discarding X-ray
binaries as the main source responsible for HeII ionization in SF galaxies.
