What is the ruling on fasting the entirety of the months of Rajab and Sha'ban?

It has not been authentically reported that the Prophet, peace and blessings be upon him, ever fasted a full month other than Ramadan. 'Aisha, may Allah be pleased with her, said: "I never saw the Messenger of Allah, peace and blessings be upon him, complete the fasting of a month except Ramadan, and I never saw him fast more in any month than he did in Sha'ban." No reliable hadith has been authentically reported regarding the virtue of fasting Rajab and Sha'ban consecutively.