The allegations - amplified by similar claims from other former pupils - have plunged the Catholic Church in Austria into its worst crisis since the war. They have accentuated divisions between conservatives and liberals, and have outraged Austria's deeply God-fearing folk, many of whom refuse to accept that they can be true.
Far from reassuring his flock of his innocence, Cardinal Groer has remained extraordinarily silent. Apart from a belated and vague statement of denial published in a Viennese paper two weeks after the allegations were made, he has refused to comment on the affair.
"In the end it is not the substance of the accusations or even whether they are true or not that has caused the greatest harm," said Wolfgang Bergmann of the Catholic charity Caritas. "It is the reaction that has really hurt. Many of the church's most active members have been left feeling uncertain, ashamed and helpless.''
At a time when the church in Austria, as elsewhere in Europe, is facing a steady decline in membership and importance, the scandal is the last thing it needed. The numbers of those leaving (around 35,000 a year out of a total membership of 6 million) is likely to increase. As Wolfgang Beilner, a theologian, warned, the church could be heading for an "unimaginable catastrophe".
It is hardly the outcome Cardinal Groer could have expected when he sat down to pen his thoughts on one of the subjects currently exercising Catholics in Austria: whether or not divorcees who remarry should be allowed to take communion. As a staunch conservative, Cardinal Groer said they should not, and in an article published in February in a church magazine, he backed up his argument by saying that no adulterers or child abusers would inherit the Kingdom of Heaven.
His comments, some of which were reproduced in Profil magazine, incensed Joseph Hartmann, a former pupil at a Catholic seminary in Hollabrunn, who claimed that as a teenager in the early 1970s, he was regularly abused by Cardinal Groer, then a teacher at the seminary. Mr Hartmann's allegations, reproduced in Profil, were then supplemented by similar claims from other ex-pupils, which in turn spawned further allegations against other clergy.
In marked contrast to Cardinal Groer, August Wanger, a Salzburg priest who was accused this month of abusing a male pupil 30 years ago, went on radio immediately and owned up. Despite the severity of his offence, Fr Wanger's honesty turned him into something of a national hero. He is still allowed to work as a teacher.
Fr Wanger's example increased the pressure on Cardinal Groer to respond to the accusations - or resign as Primate of Austria and Archbishop of Vienna. The strong liberal wing in the church also stepped up its calls for more openness.
In partial response to the criticism, the Cardinal resigned from his post as the Chairman of the Austrian Bishops' Conference earlier this month. In what many interpreted as a further attempt to limit the damage, the Vatican then appointed Bishop Christoph Schnborn to be Cardinal Groer's deputy, with automatic right of succession.
Ironically, when Cardinal Groer turned 75 last October, he submitted his resignation to Rome but was asked to stay on. Any prompt backtracking on that decision now would undoubtedly be interpreted as an admission of guilt.
Church sources in Vienna suggest that Cardinal Groer may be allowed to step down in the summer and to retire to a Benedictine monastery. In the meantime, with all those eyes still trained on him, he puts as brave a face on it as he can.