In 2005, Shi defined I-regular S-posets and used this concept to characterize PP-pomonoids and po-cancellable pomonoids. In this paper, we continued the development of the homological classification of pomonoids by using the I-regularity of S-posets. First, we characterized pomonoids over which all I-regular S-posets have one of the properties around projectivity or injectivity, and many known results were generalized. Moreover, some possible conditions on pomonoids that describe when their diagonal posets are I-regular were found. Finally, some characterizations of pomonoids by the I-regularity of their Rees factor posets were given.