Although Joan lived in a convent, she was never a nun as her father refused to allow her to take vows. She entered the convent in response to a marriage proposal from Archduke (later Emperor) Maximilian in 1472. She returned to court in 1480.
Prior to Maximilian's proposal, King Louis XI of France had wished to marry her to his younger brother Charles Duke of Berry but this proposal was also refused after Joan pointed out that if her brother died she would be the heir and throne would pass to foreigners.
It has been stated that King Charles VIII of France extended a marriage proposal in 1485 but there is no evidence and historians are skeptical. At that time he was already betrothed to Margaret of Austria, who had been sent to be raised at the French court. Charles only broke the engagement to marry Anne of Brittany in 1491.
Joan herself only seriously considered Richard III's proposal. Richard sent an emissary to open marriage negotiations on March 22, 1485, just six days after the death of his wife Anne Neville. Richard also proposed that his niece Elizabeth of York marry Joan's cousin Manoel Duke of Beja. Because Joan was a direct descendant of Philippa of Lancaster, daughter of John of Gaunt and wife of King John I of Portugal, Richard may have seen the marriage as a way of winning Lancastrian support.
Negotiations were still underway when Richard was killed at the Battle of Bosworth on August 22. Joan was reluctantly acquiescent, under enormous pressure from her brother the King who enlisted her aunt's help. Supposedly she had a dream where "a beautiful young man" told her Richard had "gone from the living." The next morning she told her brother the King that she would marry Richard if he were still alive. If not, her brother was not to press her again to marry. Shortly afterward, the Portuguese court received word of Richard's death.
According to some Portuguese authorities, after winning the English crown Henry Tudor offered marriage, but again there is no evidence.
In 1486 Joan received a second marriage proposal from the now-widowed Emperor Maximilian but she refused and returned to the convent, dying there in 1491.
Source: Barrie Williams, "The Portuguese Connection and the Significance of the 'Holy Princess,'" The Riccardian, Vol. 6 (March 1983), pp. 138-145.