Studies of X-ray continuum emission and flux variability have not conclusively revealed the nature of ultra-luminous X-ray sources (ULXs) at the high-luminosity end of the distribution (those with Lx > 1e40 erg/s). These are of particular interest because the luminosity requires either super-Eddington accretion onto a black hole of mass ~10 Msun, or more standard accretion onto an intermediate-mass black hole. Super-Eddington accretion models predict strong outflowing winds, making atomic absorption lines a key diagnostic of the nature of extreme ULXs. To search for such features, we have undertaken a long, 500 ks observing campaign on Holmberg IX X-1 with Suzaku. This is the most sensitive dataset in the iron K bandpass for a bright, isolated ULX to date, yet we find no statistically significant atomic features in either emission or absorption; any undetected narrow features must have equivalent widths less than 15-20 eV at 99% confidence. These limits are far below the >150 eV lines expected if observed trends between mass inflow and outflow rates extend into the super-Eddington regime, and in fact rule out the line strengths observed from disk winds in a variety of sub-Eddington black holes. We therefore cannot be viewing the central regions of Holmberg IX X-1 through any substantial column of material, ruling out models of spherical super-Eddington accretion. If Holmberg IX X-1 is a super-Eddington source, any associated outflow must have an anisotropic geometry. Finally, the lack of iron emission suggests that the stellar companion cannot be launching a strong wind, and that Holmberg IX X-1 must primarily accrete via roche-lobe overflow.