We present the results of Ginga observations of three narrow emission line X-ray galaxies, NGC 7172, NGC 7582 and ESO 103-G35. In each of these galaxies the column density along the line of sight to the active nucleus is extremely high (i.e. n(H) greater-than-or-similar-to 10(23) cm-2). A comparison of the optical depth in the iron K-edge with the low-energy absorption in the X-ray spectrum indicates an apparent iron abundance in excess of the solar value in these sources. Measurements of the iron K-edge energy show that the bulk of the X-ray-absorbing gas is not strongly photoionized, with only ESO 103-G35 exhibiting an edge energy significantly above that for neutral iron. In the case of NGC7582, the line-of-sight column density may have increased by a factor of approximately 3 over an interval of about 4 yr. The implications of these results for current models of the state and distribution of gaseous material in low-luminosity active galactic nuclei are briefly discussed.