Ionization of hydrogens in hypophosphorous acid
To begin with, removing another proton from anionic species is not very favorable. For example, the monohydrogen phosphate dianion is not very acidic $(\mathrm{p}K_\mathrm{a}\sim 12)$ despite it having an $\ce{OH}$ group.

In the case of $\ce{H3PO2},$ the second and third protons are bonded directly to $\ce{P},$ which is much less electronegative than $\ce{O},$ and consequently these P-H bonds are much less polarized than an $\ce{O-H}$ bond. So these protons are unable to ionize appreciably in aqueous solution.