Elul is surely a time for self-improvement and an opportunity to “get right with G-d” before the Day of Judgement. In this spirit, it is recorded that some meticulous individuals have a custom of having their mezuzot checked every year to make sure that the parchment and the letters have not been damaged.[1]
However, this custom is not obligatory; the Talmud only requires that an individual check his mezuzot every three and a half years, as you have heard. That being said, a yearly check-up is actually a good idea for mezuzot that may have sustained damage due to exposure to harsh sunlight or excessive humidity.[2] Of course, if one notices that a particular mezuzah has been affected by the elements, he should check it right away.
Aside from these set times, it is customary to check one’s mezuzot if he finds himself or his family in a “sea of troubles” or ill health. The Sages attribute special protective powers to the mezuzah, and if things are going haywire, there might be a glitch in the mezuzah force-field. Of course, it might be a good idea to check one’s moral and ethical behavior at the same time!
[1] Mateh Efraim 581:10.
[2] Aruch HaShulchan Y.D. 291:1