In Catholicism, can there ever be a reason where a bishop is removed from his office and placed back as a priest? If this can occur, what are some of the reasons it might?
The short answer: No
In Catholic Theology, ordination is tied to an indelible mark which cannot be removed. This is the same kind of idea as the indelible mark of baptism or confirmation. Through the Sacrament, God marks this souls as set aside, whether as a child of God by adoption or as a member of the clergy of His Church.
A Bishop can have his faculties stripped. The Pope can decide that a particular bishop has done something so gravely wrong that it warrants being barred from offering Mass publicly, from being given permission to ordain priests, from leading a diocese, etc. But the Bishop still retains that mark, and all of the powers that come with it.
The SSPX is a good case study of this sort of thing. Archbishop Lefebvre ordained four priests of his society as bishops. He did so illicitly, without the permission of Rome, and against the Pope's orders. He did not have permission from the Pope to do this, and he could not remain in communion with Rome after having done so, without repenting. This is why the order was considered to be in schism with Rome at that time. Lefebvre and his bishops were excommunicated, but they did not stop being bishops.
The same sort of thing happened with the Eastern Church in the schism of 1054. The Catholic Church recognizes valid apostolic succession of the bishops of the East. If the Pope could simply demote bishops, he would have demoted those Eastern ones in 1054, and the East would not have valid Holy Orders or Apostolic Succession.
Can a bishop be "demoted" to a priest?
In theory, it is possible. I am not sure this has happened, but the possibility does exists, especially if there was a case in which a bishop was consecrated in exceptional circumstances in which getting permission from the Holy See to be consecrated as a bishop was not obtained.
During the Communist era in Europe, some married individuals of the Latin Rite were ordained priests by their bishops. This threw off the Communists because they knew Roman Catholic priests had to be celibate. When Communism more or less collapsed in 1989, the Holy See ordered these men three solutions: Join an Eastern Rite where married clergy was accepted; be demoted to a the level of an active deacon in the Latin Rite and lastly be laicized.
Thus we could reason it out that the possibility of a bishop could be theoretically demoted to the level of a priest is possible. This naturally would only be done by the Supreme Pontiff, the pope.
Although sacred ordination imparts an indelible mark on the soul of a priest or bishop, priests have been known to be reduced to the level of a deacon. Both priests and bishops have had their priestly faculties taken away by Rome. Once a priest or a bishop has been ordained or consecrated, they will be forever a priest or bishop. But degradation of their position is always possible by the Holy See.
Historically there was a one time an official ceremony for the degradation of clerics.
A scandalous bishop could have bishop faculties removed, demoted to the level of a priest and could be ordered to live a life of penance in a monastery. It would not surprise me if this has in fact already occurred.
A canonical penalty by which an ecclesiastic is entirely and perpetually deprived of all office, benefice, dignity, and power conferred on him by ordination; and by a special ceremony is reduced to the state of a layman, losing the privileges of the clerical state and being given over to the secular arm. Degradation, however, cannot deprive an ecclesiastic of the character conferred in ordination, nor does it dispense him from the law of celibacy and the recitation of the Breviary. Degradation is twofold: verbal, i.e. the mere sentence of degradation; and real or actual, i.e. the execution of that sentence. They are not two distinct penalties, but parts of the same canonical punishment. Degradation is a perpetual punishment, and the clergyman so punished has never any right to release from it. It differs from deposition in so far as it deprives, and always totally, of all power of orders and jurisdiction and also of the privileges of the ecclesiastical state, thus in all things subjecting the delinquent to civil authority. While a bishop, even before his consecration can inflict deposition or pronounce a sentence of verbal degradation and can reinstate those so punished, it is only a consecrated bishop who can inflict actual degradation, and only the Holy See which can reinstate ecclesiastics actually degraded.
Solemn degradation owes its origin to the military practice of thus expelling soldiers from the army; the Church adopted this institution in order to remove grievously delinquent clerics from the ecclesiastical order. The first mention of clerical degradation is found in the eighty-third Novel of Justinian; subsequently it was adopted with its external solemnities by early medieval councils as a repressive measure against heretics. It did not originally differ from deposition, and degraded ecclesiastics were still privileged and remained exclusively subject to ecclesiastical jurisdiction. The laity, however, complained that churchmen, even when degraded, secured in this way impunity for their crimes. Hence, Innocent III (c. viii, Decrim. falsi, X, v, 20) made it a permanent rule that clerical offenders, after degradation, should be handed over to the secular power, to be punished according to the law of the land. Degradation cannot be inflicted except for crimes clearly designated in the law, or for any other enormous crime when deposition and excommunication have been applied in vain, and the culprit has proved incorrigible. According to the Council of Trent (Sess. XIII, c. iv, De ref.), a bishop, when inflicting degradation on a priest, must have with him six mitred abbots as associate judges, and three such prelates for the degradation of a deacon or subdeacon. If abbots cannot be had, a like number of church dignitaries of mature age, and skilled in canon law, may take their place. All these must give their vote, which is decisive, and must be unanimous for the imposition of so grave a penalty.
The ceremony of actual degradation consists chiefly in bringing before the ecclesiastical superior the culprit vested in the robes corresponding to his order; in gradually divesting him of his sacred vestments, beginning with the last he received at his ordination; finally, in surrendering him to the lay judge (who must always be present) with a plea for lenient treatment and avoidance of bloodshed. The words pronounced by the ecclesiastical superior during the ceremony, also other rubrical details, are laid down by Boniface VIII (c. Degradatio, ii, de poenis, in VI) and by the Roman Pontifical (pt. III, c.vii). Degradation is now rarely, if ever, inflicted; dismissal, with perpetual deprivation, takes its place. - Degradation (Catholic Encyclopedia)
In the Middle Ages, there existed a Pontifical ceremony reserved to the pope for the removal of the red hat of a cardinal by the pope himself. Thus the cardinal lost his rank of a Prince of the Church.
It is a ceremony that was employed at least on one occasion, unfortunately I can not recall the situation at the moment. What I can recall of the ceremony is that the cardinal in question walked into the pope’s presence wearing his red hat and bare-footed. When he reached the Holy Father, the pope removed his red hat, admonished him and finally pronounced the bishop or priest to no longer to be a cardinal.