I am sure that they must still exist. Clare was a protege of Francis, and their tight bond was probably motivated by their belief in the need for the new way of life he was establishing. It makes sense that people in religious life would still have have close affiliations with people of the opposite sex who share their same aspirations too. Other partnerships I think of are Benedict and his sister Scholastica, and Teresa of Avila’s collaboration with John of the Cross in reforming the Carmelite order and opening new monasteries and convents.
I think there is less of a tendency to highlight the close working relationships of relgious people, because of our society’s tendency to sexualize everything, and maybe this make people more hesitant to divulge insights and support in endeavors that they receive from some one of the opposite sex.
I also think that in modern times, it is much easier to communicate with people, whereas during the life times of the previous “couples” mentioned, it took much greater effort and time for correspondence, so that the circle from which one received inspiration was probably much smaller and easier to indentify.