The question as to why the Gemora uses the requirement of the checking Mezuzois twice in seven years is puzzling. If one starts the seven year cycle that in years, two and four there is a check, and then in the second cycle in year five and seven, there would be a gap of more than 7 years.
Why could the Gemora simply say once every three and a half years? Surely the excuse of not mentioning 'halves' is unsatisfactory as we know that the Tekufois are stated in half months.
Shloem, UK
1) I think that the simple pshat is that Chazal did not require us to be so precise in the times for checking the mezuzah. Rashi writes here that the reason it must be checked is because it might have been stolen or may have decomposed. Well, both those possibilities are not so frequent but we still want to make sure every so often that everything is OK with the mezuzah. Now a period of 7 years is a significant period of time, and we often find in the Gemara that when Chazal want to mention a period of time which is significantly longer than a year that they mention 7 years. 7 years is a "week" of "years" and is a significant period in history. Chazal said that it is not sufficient to check it once every 7 years because there is a reasonable chance that it was stolen or decayed before then, but twice in 7 years is a reasonable frequency. People remember the 7-year cycle, possibly because of the Shemitah year, so it will be eaiser for people to follow the twice in 7 rule than once in 3 and a half; since 3 and a half is a harder number to remember than the number 7. We are not worried that a person will check it in the 4th year of the first cycle and the 5th year of the second cycle, and even if they would occasionally do that it probably would not be a disaster since usually the mezuzah does not get stolen or decay.
To summarise the above; the crucial thing is to give people an easy number to remember. Twice in 7 is easier to remember than once in 3 and a half.
2) In the way of drash, I saw a beautiful explanation (in the sefer Uri Tzafon page 290) given by Rav Isser Dov Kook of Tiveriya (the son-in-law of Rav Yitzchak Zilberstein shlita). There is another Halacha that comes twice in every 7 years; that is the Mitzvah of giving Maaser Oni to the poor, which is given in the 3rd and 6th year of every Shemitah cycle. The Mezuzah is also a sign of how temporary we are in this world. The Rambam in Hilchos Mezuzah 6:13 writes that when we see the Mezuzah every time we go in an out of our house, we wake out of our sleep and forget the vanities of this world. The only thing that stays for ever and ever is the knowledge of the Rock of the World. Even the strongest and most impressive building does not last forever. It is only what the Mezuzah represents that lasts forever. The Mezuzah is a reminder of how poor we really are, if all we have is a palace without the awareness of Hash-m. So Mezuzah is similar to Maaser Oni because it must be checked twice every 7 years to remind us that however rich our house seems to be we are spiritual paupers if we do not think regularly about what it says in the Mezuzah.
Wishing you a good Pesach Sheni.
Dovid Bloom
Thank you for your constant inspirational responses.
My father suggested that the chiyuv is really once every seven years. However, it does not suffice to do this once as this might end up being a cursory exercise. What is required is a 'double' check, to read and re-read the words. In other words 'TWICE' in the seven years. Perhaps the words of the Tiferes Yisroel in Avos in respect of the publication of seforim rings true and would support this answer.
Sholem
1) There is a question on this because in Maseches Mezuzah (which is one of the short Masechtos printed at the end of Maseches Avodah Zara) it says that a Mezuzah has to be checked once in 25 years. In order that this should not disagree with our Gemara we can say that Maseches Mezuzah is referring to a Mezuzah in a public place. According to this we see from Maseches Mezuzah that it is checked once in 25 years, not once twice over in 50 years. If so, the private mezuzah should be checked twice in 7 years, not once twice over in 7 years.
2) The Tiferes Yisrael Avos 2:2 in Boaz, suggests that certain Masechtos were not checked over, because of lack of time. However, I think there is a difference between checking a sefer before publishing it, and between checking a Mezuzah, since the Beis Yosef Orach Chaim end #39 DH uTefilin cites our Gemara and writes that the check that it is required is not to see if it was written in the first place with extra or missing letters, but rather to determine if the words have worn out or become destroyed by the elements in the meantime.
KOL TUV
Dovid Bloom