For an explanation of the methodology of this series, see the introduction.

"Any person who becomes unclean from [contact with] the dead, or is on a distant journey, whether among you or in future generations, he shall make a Passover sacrifice for the L-rd" (Num. 9:11)

Rashi: "On a distant journey"
There is a dot over the word "rechoka" [meaning "distant"] to teach us that he does not really have to be far away, but even if he was merely outside the threshold of the Temple courtyard throughout the time allowed for the slaughtering of the Passover sacrifice. On the second Passover, one may keep both leavened bread and unleavened food in the home, and there is no festival (i.e. all forms of work are permitted). The consumption of leaven is not forbidden except while he eats the sacrifice.

Pesach Sheni... represents the path of teshuvah.

The Lubavitcher Rebbe: Pesach Sheni represents compensation or correction for a prior shortcoming, and thus represents the path of teshuvah. This is [also] seen in the difference between the first and second Passovers:
(1) Chametz is the evil and forbidden. Nevertheless, Rashi states that on Pesach Sheni one can keep both chametz and matzah in one's home, hinting that teshuvah can elevate one's past forbidden acts.
(2) The first Passover is one week long, showing a gradual spiritual ascent, while Pesach Sheni is only one day, showing the power of teshuvah to elevate and transform in a single moment.
Teshuvah has the power to wipe out a person's past deeds, and transform him into a new person. This is the inner reason that the 2nd Passover offering, representing correction and compensation for the mistakes of the past, was recorded out of chronological order, because teshuvah has the power to rearrange a person's life out of chronological order, wiping away his past mistakes. (Likutei Sichot 23, 70-17) is distant because he or she is "unclean."

BeRahamim LeHayyim:
"A distant journey": Literally this means physical distance, but the Zohar looks at this spiritually, meaning that one is distant because he or she is "unclean." Perhaps we can take it even one step further: one's heart is not in the proper place when Passover time comes in — one is estranged from one's self. "Far out, man!"
G‑d desires the heart. And G‑d gives us a second chance if we are not in the right mind-space when it is time to get rid of all chametz, when it is time to offer the Passover sacrifice.
What an amazing idea: that when we are ready, we can rectify/heal/fix that which is needed. G‑d gives us the extra month between 14 Nissan and 14 Iyar to get ourselves together.