We present multi-epoch mid-infrared (IR) photometry and the optical discovery observations of the "impostor" supernova (SN) 2010da in NGC. 300 using new and archival Spitzer Space Telescope images and ground-based observatories. The mid-infrared counterpart of SN. 2010da was detected as Spitzer Infrared Intensive Transient Survey (SPIRITS). 14bme in the SPIRITS, an ongoing systematic search for IR transients. Before erupting on 2010 May 24, the SN. 2010da progenitor exhibited a constant mid-IR flux at 3.6 and only a slight similar to 10% decrease at 4.5 mu m between 2003 November and 2007 December. A sharp increase in the 3.6 mu m flux followed by a rapid decrease measured similar to 150 days before and similar to 80 days after the initial outburst, respectively, reveal a mid-IR counterpart to the coincident optical and high luminosity X-ray outbursts. At late times, after the outburst (similar to 2000 days), the 3.6 and 4.5 mu m emission increased to over a factor of two. times the progenitor flux and is currently observed (as of 2016 Feb) to be fading, but still above the progenitor flux. We attribute the re-brightening mid-IR emission to continued dust production and increasing luminosity of the surviving system associated with SN. 2010da. We analyze the evolution of the dust temperature (T-d similar to 700-1000 K), mass (Md similar to 0.5-3.8 x. 10(-7) M circle dot), luminosity (L-IR similar to 1.3-3.5 x 10(4) L circle dot), and the equilibrium temperature radius (R-eq similar to 6.4-12.2 au) in order to resolve the nature of SN. 2010da. We address the leading interpretation of SN. 2010da as an eruption from a luminous blue variable high-mass X-ray binary (HMXB) system. We propose that SN. 2010da is instead a supergiant (sg)B[e]-HMXB based on similar luminosities and dust masses exhibited by two other known sgB[e]-HMXB systems. Additionally, the SN. 2010da progenitor occupies a similar region on a mid-IR color-magnitude diagram (CMD) with known sgB[e] stars in the Large Magellanic Cloud. The lower limit estimated for the orbital eccentricity of the sgB[e]-HMXB (e > 0.82) from X-ray luminosity measurements is high compared to known sgHMXBs and supports the claim that SN. 2010da may be associated with a newly formed HMXB system.