We present results based on observations of SN 2015H which belongs to the small group of objects similar to SN 2002cx, otherwise known as type Iax supernovae. The availability of deep pre-explosion imaging allowed us to place tight constraints on the explosion epoch. Our observational campaign began approximately one day post-explosion, and extended over a period of about 150 days post maximum light, making it one of the best observed objects of this class to date. We find a peak magnitude of M = −17.27± 0.07, and a (Δm$\mathrm{<mrow\; data-mjx-texclass="ORD">15</mrow>}$) = 0.69 ± 0.04. Comparing our observations to synthetic spectra generated from simulations of deflagrations of Chandrasekhar mass carbon-oxygen white dwarfs, we find reasonable agreement with models of weak deflagrations that result in the ejection of ~0.2 M$\mathrm{<mrow\; data-mjx-texclass="ORD">\odot </mrow>}$ of material containing ~0.07 M$\mathrm{<mrow\; data-mjx-texclass="ORD">\odot </mrow>}$ of $\mathrm{<mrow\; data-mjx-texclass="ORD">56</mrow>}$Ni. The model light curve however, evolves more rapidly than observations, suggesting that a higher ejecta mass is to be favoured. Nevertheless, empirical modelling of the pseudo-bolometric light curve suggests that ≲0.6 M$\mathrm{<mrow\; data-mjx-texclass="ORD">\odot </mrow>}$ of material was ejected, implying that the white dwarf is not completely disrupted, and that a bound remnant is a likely outcome.