From the moment when Blessed Paul VI intervened and stripped them of their ministry for their lack of submission to him as Vicar of Christ in 1976, because they disobeyed a direct command from the Successor of Peter, they could have returned to communion with Rome…a communion they ruptured by gross and flagrant disobedience.
We pray that they return to communion with Rome. They’ve persisted in this state for more than 40 years. EWTN has a summary of the Society’s history; I add a few underscores of special importance.
*The Society of St. Pius X (SSPX)
The Society was founded in 1970 by Archbishop Marcel Lefebvre, a retired missionary bishop who had served in Africa, in order to perpetuate the traditional liturgical rites of the Church. The previous year Blessed Paul VI had introduced a new missal in response to the liturgical reform called for by the Second Vatican Council. Reformed rites of the other sacraments would follow in the years following.
While Archbishop Lefebvre did not reject the possibility of reforming the sacramental rites (he had voted for the Council document that called for it), he did reject the specific reforms of the Mass promulgated in 1969 in the Missal of Paul VI. For this reason, the Society he founded uses the 1962 Missal and the other sacramental ritual books of that era.
In 1971 Archbishop Lefebvre started a seminary in Ecône, Switzerland, to train priests for the Society. Despite being specifically warned by the Pope not to ordain them, the Archbishop ordained the first ones to the priesthood in 1976. Those ordinations were valid, but illicit. Pope Paul VI immediately suspended the Archbishop’s priestly faculties, and those of the men he had ordained. Those suspensions remain effective, and apply to all new ordinands of the Society, until such time as the Holy See regularizes the status of the SSPX and its clergy.
In 1989, Archbishop Lefebvre, now fearing that he would die and leave no one to ordain priests for the SSPX, sought an agreement with the Holy See for the lawful continuation of the Society. After reaching an agreement with Cardinal Joseph Ratzinger, acting for Pope St. John Paul II, Archbishop Lefebvre broke the agreement and, in an act which was ipso facto schismatic, ordained 4 bishops without a papal mandate. This action incurred an automatic excommunication under canon 1387, confirmed a few days later by Decree of the Holy See. Twenty years later (January 2009), as part of another effort at reconciliation on the part of Rome, Pope Benedict XVI lifted these excommunications. Despite this, to date reconciliation has not been achieved.
Therefore, until the status of the SSPX is regularized by the Holy See, the bishops and priests of the Society remain suspended from the exercise of Holy Orders. Their celebration of the sacraments are valid but illicit,
except for those sacraments requiring jurisdiction (Penance, Marriage), which are both invalid and illicit. This means that sacramental absolution by a Society priest is invalid for lack of jurisdiction, a requirement in all circumstances but the danger of death (canon 976). Similarly, lacking jurisdiction, marriages witnessed by SSPX clergy would also be invalid, for defect of the “Catholic form”, which requires witnessing by one’s bishop or proper pastor or a dispensations for other circumstances (canon 1108)
Priestly Fraternity of St. Peter (FSSP)
In the circumstances of the 1989 episcopal ordinations, some SSPX clergy and seminarians, not wanting to go into schism, sought an agreement with the Holy See. This request resulted in the founding of the Sacerdotal (Priestly) Fraternity of St. Peter (FSSP)
ewtn.com/expert/answers/sspx_fssp.htm*
Pope Benedict explains the history of the Motu Proprio of his predecessor:
*At the time, the Pope primarily wanted to assist the Society of Saint Pius X to recover full unity with the Successor of Peter, and sought to heal a wound experienced ever more painfully. Unfortunately this reconciliation has not yet come about.
I now come to the positive reason which motivated my decision to issue this Motu Proprio updating that of 1988. It is a matter of coming to an interior reconciliation in the heart of the Church. Looking back over the past, to the divisions which in the course of the centuries have rent the Body of Christ, one continually has the impression that, at critical moments when divisions were coming about, not enough was done by the Church’s leaders to maintain or regain reconciliation and unity. One has the impression that omissions on the part of the Church have had their share of blame for the fact that these divisions were able to harden. This glance at the past imposes an obligation on us today: to make every effort to enable for all those who truly desire unity to remain in that unity or to attain it anew.
Needless to say, in order to experience full communion, the priests of the communities adhering to the former usage cannot, as a matter of principle, exclude celebrating according to the new books. The total exclusion of the new rite would not in fact be consistent with the recognition of its value and holiness.
Each Bishop, in fact, is the moderator of the liturgy in his own Diocese. Nothing is taken away, then, from the authority of the Bishop, whose role remains that of being watchful that all is done in peace and serenity. Should some problem arise which the parish priest cannot resolve, the local Ordinary will always be able to intervene, in full harmony, however, with all that has been laid down by the new norms of the Motu Proprio.
w2.vatican.va/content/benedict-xvi/en/letters/2007/documents/hf_ben-xvi_let_20070707_lettera-vescovi.html*