The internal chronology of Minami-ke is, like many other anime and manga, neither particularly careful nor exact. Minami-ke is not achronological, because events have clear consequences, and there are no unexplained resets as the series progresses. However, the anime as it currently stands is exceedingly unlikely to be in normal chronology, due to certain internal contradictions that can only be rationalized with difficulty. It is most likely that the anime follows what is commonly known as "Calvin and Hobbes" (or "Simpsons") time, in which the seasons progress, new characters are introduced, and so forth, but no one ages, no major life events occur, and the status quo is never significantly altered.
The manga, on the other hand, has no difficult contradictions, but progresses at such an exceedingly slow pace that it is easily plausible to assert that it follows the same strategy, especially given that, besides seasons, it never refers to any specific date or time, not even to mention school breaks. At the very least, it doesn't follow chronological order.
Season one has a relatively straightforward chronology, apparent from the wall calendars liberally distributed around the Minami Residence. The episodes transition smoothly from a start on October 14th 2007, through a switchover to November in Episode 10, to an end on December 31st 2007. The only exceptions are Episode 05 and Episode 09, which take place in July-August 2007.
No such timing is done in the manga and, as a result, a few chronological mistakes filter into the anime, most notably the contradiction betweenMaki's seemingly sincere belief in Episode 04 (October 2007) that Haruka has two children, never having met Kana or Chiaki, and her casual, familiar greeting of those very same sisters in Episode 05 (July 2007). There is also the flashback in Episode 07 to a sixth grade Kana with long pigtails, while in Minami-ke Chapter 078 she has short pigtails for the middle school entrance ceremony. This is, of course, less severe.
OkawariSeason two occurs over a much more restricted time period, January and February of 2008, again by observation of calendars. The calendars give no year, but given the girls' familiarity with Touma, Fujioka, and Mako-chan, it must occur after season one, and it seems most reasonable to assert that it occurs directly after season one, in what should be early 2008, especially given that the pattern of days in "January" match January 2008.
One minor inconsistency is Chiaki's easy participation with Haruka in a three-legged race in the anime-original Episode 11. In Minami-ke: Okaeri Episode 07 (Minami-ke Chapter 090), Chiaki is shown to be very poor at the practice. Of course, this could easily have been due to Makoto's involvement in the latter...
The third season is where the anime arguably breaks from even any attempt at chronology, and where it may even be attempting to disguise the fact. Calendars are absent throughout the season, and Chiaki's grade-identifying class number, 5-2 (fifth grade, class two), previously seen throughout her classroom, is completely expunged, appearing only once, in a flashback.
If the third season were indeed chronological then, like the second season, it is forced by the early presence of Touma to occur after season one. Episode one occurs on New Years. If this is New Years 2008, the earliest it can possibly be, then every character should advance a grade in February/March, and Hosaka and Hayami should graduate. Instead, both are seen wandering the halls well after the "Spring" implied by the episode ordering.
In addition, the third season and OVA brings up not one, but two Valentine's Days involving Kana. Combined with Okawari, the holiday has occurred a total of three times, with Kana clearly in middle school in each case. Given that the series started with her in the second year, this is impossible.
Finally, and most minor, Chiaki's school holds an athletic festival only half a year after the one in Okawari. Either the date was shifted, or the school holds two a year, both implausible practices.
These contradictions can be justified by a combination of highly contrived explanations (two of those Valentine's Day were really the same Day, every scene with Hosaka in late Okaeri is a flashback), but the most reasonable assumption is simply that the series is now in Calvin and Hobbes Time.
In the manga, happily, no contradictions have yet surfaced. Valentine's Day has only happened twice, and no seasonal event has happened an implausible number of times. However, given the extremely slow pace of events, the manga's achronological chapter order, and the clear lack of intention to do anything that would majorly affect the current state of affairs (i.e. Fujioka will never get through to Kana), it is easy to assume that the manga, like many comedy mangas, is frozen in time the same way the anime is.