More precisely, a lack thereof. I briefly glanced at an article I found at snpp.com complaining of the tendency from episode to episode for Homer to revert back to an archetypal American male chauvanist after developing more into a progressive SNAG (Sensitive New-Age Guy). Such reversion between episodes, she argued (and who else would make this argument but a she? ;D ), underlied the permanence of the male characters wallowing in "their masculine/piggish rut."
However, if I may be so bold, I might, and in fact to a small degree shall, contend that this discontinuity between the more sensitive Homer at episode's end to the so-called "jerkass" Homer of the next episode's beginning is simply the manifestation of the Sisyphus myth. Whatever progress Homer has made in one episode, rolling his boulder from the valley of "jerkass"ness near to the summit of 'modern-day liberal man', must be continually remade in later episodes as the boulder comes tumbling back down.
The motivation for this Sisyphean trope is twofold. First, it is too familiarize Homer's struggles with someone who is not a 'die-hard' follower of the series. One can simply begin watching an episode and understand the nature of Homer's struggle without needing to be versed in the layered intricacies of the show and its characters.
The second reason ties in with the Simpsons's tendency towards postmodern fragmentation. Life is not a continuous, unbroken, contained duration, but is made up of a series of discrete episodes strung together to mimic movement through time, much like the dynamics of film, aka 'moving pictures.' Because lives are thus segmented, it is inreasingly likely that lessons will be forgotten from episode to episode; that one learns something in one episode does not guarantee that the lesson will carry over into later episodes.
Homer's perpetual struggle illuminates for us our own fragmentation in the course of our lives. Though his initial chauvanism antagonizes us, his development to a stage we feel is more progressive gradually elicits our sympathies from him -- we become that much more involved in his evolution. In watching the various Sisyphean permutations he must go through, we see in Homer's endeavors our own lives: the endless struggle towards a more enlightened self, the journey's numerous setbacks never deterring its resumption. After all the perseverance, in the end, we find hope for ourselves.
Prof. 444