I remember reading about this in Chabad CHassidus, either in Torah Ohr/ Likutei Torah or Samech Vav (somewhere), but based on what I remember from there, and many other places in chassidus (which may be easier to find), the fact that the Hei is missing is related to the fact that the four (/five, see below) descriptions of the soul mentioned, "[the] soul that you've placed in me, it is pure, you have created it, you have formed it, and you have breathed it into me", those four terms refer, respectively, to how the soul exists in 4 different universes (at the same time):
pure: the world of Atzilus, which is tecnically within the category of limitation in some way, but is almost entirely G-dliness, "pure" from all evil and separation
created: this refers to how the soul exists in the universe of "Briah"/creation, which is the first universe that has some kind of independant existance ("creation"), although everything that exists there is still very spiritually-close together, and there is still not much separate.
formed: THis is how the soul exists in the next universe down, called "Yetzira"/formation, and, as the name suggests, everything in the universe has a separate spiritual "form" of its own, there exists unique entities.
breathed it into me: this is how the soul exists in the lowest of the four spiritual worlds, Asiyah (/action), and this universe everything has more separate than before, there exists more possibility for evil, and the things that are happening in this (physical -- see below) universe are influenced by this world directly.
And the fifth description: and you guard it within me: refers to how the soul exists in this actual, physical universe, inside a real, physical body.
SO: The four worlds refer to the four letters of Hashem's name, Yud, Hei, Vav, Hei, so I'm pretty sure that I read in either Torah Ohr/Likutei Torah or one of the Rebbe Rashab's Mamaarim, or it might have (also) been a Maamar somewhere in the Rebbe's Melukit Mamaarim, that the four levels of the soul refer to the four worlds AND also the four letters of Hashems name (and the last, fifth level is somewhat related to the second "aspect" of the lower "Hei" which is discussed a lot in Chassidus), and the first thing mentioned - "Neshama" refers to how the soul exists beyond all of the other worlds, in the essence of Hashem, which the essence of Hashem is not limited or described by any name or letter.
And that's also related to the fact that the last description of the soul "you guard it within me" also isn't associated with a specific letter (entirely), because it is linked to the first description -- "Neshama" because the main power of the soul, from it's source in the Essence of Hashem, is given to the level of the soul that's in the body, specifically. (See the Basi Legani 5742 Maamar for more on this last point).
So that's why there's no Hei, because it's referring to the soul in the essence of Hashem.