It isn't accurate or reliable in any way whatsoever. The first mention we ever have of this story comes from a letter from Fray Antonio de Guevara to Garci Sánchez de la Vega. The letter does not have any date, probably because Guevara forgot to write it down in his copying book, something that happens to everyone every so often. Back to Guevara, his letters were published for the first time in August 1539, in Valladolid, by Francisco Fernández de Córdoba. Guevara was a very known scholar, who had been translated into a number of languages, so his letters would have been an instant best-seller.

As Fray Antonio de Guevara mentions in the letter that he was visiting the populations of the Kingdom of Granada after having baptised 27,000 houses of moriscos in Valencia, we can date the letter in the years 1525-26. This is 35 years after the alleged fact, bear that in mind. It's still within living memory, but very far apart from the facts commented. I'll translate Guevara's version of the fact, with the incorrect grammar the old morisco has:

Coming to the point, you should know, my lord, that in this visit I have ten crossbowmen with me, both as guards and so that they show me this land. And, as I climbed a hill from which you lose sight of Granada and get sight of Valdeleclín, an old morisco that came with me spoke this badly composed words: «If want you, alfaqui, stop here little little and me tell you thing big that boy king and mother his do here»

From here on, Guevara tells, in good Spanish prose, the story of the moor's sigh. The words normally put on Aixa's mouth, however, differ in Guevara's account from the usual formulation one normally sees in Spanish. I transcribe and then translate:

Justa cosa es que el rey y los caballeros lloren como mugeres, pues no pelearon como caballeros

Translation: Fair thing it is that the King and his knights shall cry like women, for they did not fight like knights.

Then Fray Antonio de Guevara adds a comment he puts in the old morisco's mouth: Many times I heard the boy king, my lord, say that had he known what his mother would later say about him and his knights, they would have killed eachother or turned back to Granada to fight.

This comment pretending to give credibility to the story, somehow destroys it entirely. This old morisco, allegedly says that he spoke many times with Boabdil after that fact, which means that he would have accompanied him to exile, and then come back to Spain. We know Boabdil was exiled in 1493, and that is when the story should have happened. He went to exile with his family and only a few close courtiers. The courtiers in Granada would have spoken Spanish more than reasonably well, like Yusuf ibn Kumasa, Abrahem al Cayci, or Abrahem el Pequeni, as they would serve both as court officers and occasionally as diplomats, having to speak mostly to the Kings of Castile. Pretending that a courtier would speak such a dreadful Spanish as shown at the beginning of the story is not credible.

The story is good, and it ends with an aesop about knighthood, so we can place it in the same category as fables or exempla, a genre well known in Spanish literature through El conde Lucanor, by Don Juan Manuel, prince of Villena.