What is the history and explanation as to why the "diaconate" was MIA in the Western Church over a certain period of time? The Catechism of the Catholic Church implies that over a certain time in the period in the Western Church, there weren't any deacons.


  CCC 1571 Since the Second Vatican Council the Latin Church
  has restored the diaconate "as a proper and permanent rank of the
  hierarchy," while the Churches of the East had always maintained it.


What is the history and explanation behind this?

The good answer will also correct any wrong assumptions.
It was not deacons, but "permanent deacons," who disappeared for a while. In this answer I will summarize and quote from an article titled Called to Serve: The Mission of the Permanent Diaconate by Deacon Michael Chesley.


  Although the permanent deacon is a relatively new occurrence
  experienced on the altars of many U.S. dioceses around the country,
  deacons in general are nothing new to the Church.


Chesley summarizes the early development and documentation of the role of deacons. As the catechism says (1570), "Among other tasks, it is the task of deacons to assist the bishop and priests in the celebration of the divine mysteries, above all the Eucharist, in the distribution of Holy Communion, in assisting at and blessing marriages, in the proclamation of the Gospel and preaching, in presiding over funerals, and in dedicating themselves to the various ministries of charity."


  However, by the time of Pope Gregory the Great in 595 A.D, many of
  these duties already began to be heavily curtailed or delegated to the
  minor orders.  Although it is beyond the range of this article to
  cover a detailed account of the reasons for the decline of the order,
  suffice to say that their [sic] was a gradual occurrence of men who
  preferred not to remain a deacon all their lives, and wanted to
  advance to the higher orders.  By the middle ages, the order of deacon
  as a permanent rank in the hierarchy of the Church all but disappeared
  in the West, and became nothing more than a stepping stone for
  preparation to the priesthood.  Although not widely known, the Council
  of Trent (1545 – 1563) called for the restoration of the permanent
  deacon. Unfortunately the idea was never followed through, and it was
  not until the Second Vatican Council that the Church in the West took
  up the wishes of Trent some 400 years later.
  
  ...
  
  Although the Latin Rite Church had "transitional" deacons, the Council
  goes on to say that the Church envisions what it hoped would be a
  permanent rank reestablished within the Latin Church.  One could ask
  why did the Church desire to restore the order of deacon as a
  permanent rank at this point in church history? The Directory for the
  Ministry and Life of Permanent Deacons addresses this question as
  follows: "One of the fruits of the Second Vatican Council was the
  desire to restore the diaconate as a proper and stable rank of the
  hierarchy". On the basis of the "historical circumstances and pastoral
  purposes noted by the Council Fathers, the Holy Spirit, protagonist of
  the Church's life, worked mysteriously to bring about a new and more
  complete actualization of the hierarchy which traditionally consists
  of bishops, priests and deacons. In this manner the Christian
  community was revitalized, configured more closely to that of the
  Apostles which, under the influence of the Paraclete, flourished as
  the Acts of the Apostles testifies."*
  
  ...
  
  Although for many centuries the deacon ascended to higher orders after
  ordination to the diaconate, there still exist "transitional" deacons
  and "permanent" deacons. However, there is no sacramental difference
  or function between the two.  Under normal circumstances, when the
  permanent deacon path is chosen, the deacon remains in his chosen
  vocation.


Also at Vatican II, married men were permitted to become deacons. Unmarried men becoming deacons are still required to take a vow of celibacy, however.

* Chesley's source for this quote is given as: Congregation for Catholic Education; Congregation of the Clergy; Directory for the Ministry and Life of Permanent Deacons. ( Libreria Editrice Vaticana 1998), Chapter III.