During September of 2016, I wrote a series of computer programs to calculate the MOID value for two arbitrary orbits. One result of this work was a daily-updated listing of all NEOs with their MOID values for the inner five planets (available here).
For specific objects of interest, I was able to compute the variation in the value of the closest approach at different times of the year. As an example for the PHA (2340) Hathor, the following chart shows a close approach of 0.10 A.U. in mid-January as the object crosses the Earth's orbit inbound, and an even closer approach on October 20 as the object crosses the Earth's orbit outbound. The closer of the two approaches is the MOID, which is presently 0.0069 A.U.
Since orbits change with time due to perturbations, the associated MOID will change too. The following chart shows the change in the MOID of (2340) Hathor, from 0.0091 A.U. in 1900 to 0.0033 A.U. in 2200. Four close approaches during this interval are included. The 1976 and 2086 events are very close to the MOID values for those years, suggesting that these approaches were as close as they could be.
See also my MOID Random Thoughts page