While much of the first four centuries of Church History concern the deity of Christ, His relationship with the Father, the nature of the union of God and Man, and even the generation of the Son, less attention was paid to the development of the Holy Spirit, or the 3rd Person of the Trinity. For most of the formative years, the Holy Spirit was not seen as a separate person, and indeed, during the great debates of the 4th century, was pushed to side as a topic. It was only after the council in 381 that a doctrine of the Spirit as an entity separate and distinct from the Father and the Son began to develop.
Note, if you allow for doctrinal development, the most rational answer is that the notion was always there, but only came to be known some 300 years after the Apostles wrote the New Testament. If you don’t allow for doctrinal development then it is difficult to actually place the notion of the distinction in the Godhead of the Spirit, unless you backwards apply terminology and context, and allow for nonliteral translations. While it may be expedient to state the the doctrine of the Holy Spirit is clear in the Scriptures, it is dishonest – as it is only clear through terminology and theology developed as the Church developed. Further, many of the English translation compound the doctrinal matter by using the masculine pronoun when only the gender neutral (it) pronoun is called for. Adding to this is mistranslations as such which is found in Hebrews 10.15, which is singled out in early debates as a sign that the Spirit is God.
As R.J. Wright, note,
The vagueness of the scriptural evidence concerning the Holy Spirit in the early Church, especially regarding the Spirit’s identity and distinction from the Son, was noted as early as St. Gregory Nazianzen in the later fourth century, who remarked that Scripture itself does not “very clearly or very often call the Spirit God in so many words, as it does call God first the Father and later on the Son.” Indeed, before the Second Ecumenical Council added the third paragraph to the Niceno-Constantinopolitan Creed in 381, most creeds both eastern and western ended simply with the words “and in the Holy Spirit.” In fact, it is not entirely certain that the entire expanded form of the third paragraph as we have it actually came from Constantinople in 381.
As Swete and others noted, when the Spirit was discussed it was seen in a drastically subordinated role to the Son. The doctrine was simply left to whether, undeveloped, until the end of the Fourth Century. Even as late as 380, Gregory Nazianzus said,
“Of the wise among us, some consider the Holy Ghost an influence, others a creature, others God himself and again others know not which way to decide, from reverence, as they say, for the Holy Scripture, which declares nothing exact in the case. For this reason they waver between worshipping and not worshipping the Holy Ghost, and strike a middle course, which is in fact, however, a bad one.”
It was Gregory which helped to push for the full development of the doctrine. He would say, in explaining the development of the doctrine thus far,
“The Old Testament proclaimed the Father manifestly, and the Son more hiddenly. The New manifested the Son, and suggested the deity of the Spriit. Now the Spirit himself is resident among us, and provides us with a clearer explanation of himself.” (Oracles 31.26)
Early, he conceded that Scripture did not “very clearly or very often call him God in so many words, as it does first the Father and later the Son.”(Or 31.21)
In arguing for the deity of the Son, Athanasius would say,
“If we must take our knowledge of the Spirit from the Son, then it is appropiate to put forward proofs which derive from him (the Son).”
For Athanasius, this proved that the Son was indeed God since the Spirit came from God Himself.
Jaroslav Pelikan, in his first volume, writes,
“Development of such a doctrine (Trinity) was the achievement of the same men whose doctrine of the Holy SPirit we have been considering, especially the so-called Cappadocians, Basil, Gregory of Nazianzus, and Gregory of Nyssa.”
It is simply a matter of history that as the Church developed the doctrine of the Trinity, the Holy Spirit was, as others had noted, a ‘step-child’ doctrine.
At least one Trinitarian scholar has admitted: The language of the New Testament permits the Holy Spirit to be understood as an impersonal force or influence more readily than it does the Son…The attempt to develop an understanding of the Holy Spirit consistent with the Trinitarian passages…came to fruition at Constantinople in 381. There were a number of reasons why the personhood of the Holy Spirit took longer to acknowledge than the Son: (1) the term pneuma, breath, is neuter in general and impersonal in ordinary meaning; (2) the distinctive work of the Holy Spirit, influencing the believer, does not necessarily seem as personal as that of the Father…in addition, those who saw the Holy Spirit as a Person, were often heretical, for example, the Montanists; (3) many of the early theologians attributed to the Logos or Word, the revelatory activity later theologians saw as the special, personal work of the Holy Spirit
Notice the following:
Roman Catholic and Orthodox theologians agree in recognizing a certain anonymity characterizes the Third Person of the Holy Trinity. While the names Father and Son denote very clear personal distinctions, are in no sense interchangeable, and cannot in any case refer to the common nature of the two hypostases, the name Holy Spirit does not have that advantage. Indeed, we say that God is Spirit, meaning by that the common nature as much as any one of the persons. We say that he is holy…Taken in itself, the term Holy Spirit thus might be applied, not to a personal distinction…In that sense, Thomas Aquinas was right in saying that…the name Holy Spirit has been given to him…we find an image of the economy of the Third Person rather than an image of his hypostatic character: we find the procession of a divine force or spirit which accomplishes sanctification. We reach a paradoxical conclusions: all that we know about the Holy Spirit refers to his economy; all that we do not know makes us venerate him as a person
 Or, emanation
 History of the Christian Church, Volume III: Nicene and Post-Nicene Christianity. A.D. 311-600.
 Brown HOJ. Heresies: Heresy and Orthodoxy in the History of the Church. Hendrickson Publishers, Peabody (MA), 1988, p. 140
 Clendenin D.B. ed. Eastern Orthodox Theology, 2nd ed. Baker Academic, 2003, pp. 165-166