This hadeeth was narrated from the Mother of the Believers ‘Aa’ishah (may Allah be pleased with her) who said: 

The Messenger of Allah (blessings and peace of Allah be upon him) used to fast three days every month, and sometimes he would delay that until a year’s fasts accumulated and sometimes he would delay it until he fasted Sha‘baan. 

This was narrated by at-Tabaraani in al-Mu‘jam al-Awsat, 2/320. He said: Ahmad told us: ‘Ali ibn Harb al-Jandeesaboori told me: Sulaymaan ibn Abi Hawdhah told us: ‘Amr ibn Abi Qays told us: from Muhammad ibn ‘Abd ar-Rahmaan ibn Abi Layla, from his brother ‘Eesa, from his father ‘Abd ar-Rahmaan, from ‘Aa’ishah who said. Then he quoted it, then he said: This hadeeth was not narrated from ‘Abd ar-Rahmaan ibn Abi Layla except via this isnaad, and ‘Amr is the only one who narrated it. End quote. 

This is a da‘eef (weak) isnaad because of Muhammad ibn ‘Abd ar-Rahmaan ibn Abi Layla – the famous faqeeh – of whom Imam Ahmad said: He had a poor memory and his narration of hadeeth was inconsistent. Shu‘bah said: I have never seen anyone with a poorer memory than Ibn Abi Layla. ‘Ali ibn al-Madeeni said: He had a poor memory and his hadeeth is weak. Hence the scholars classed this hadeeth of his as da‘eef. 

Al-Haythami (may Allah have mercy on him) said: 

Its isnaad includes Muhammad ibn Abi Layla and there are some reservations concerning him. End quote. 

Majma‘ az-Zawaa’id, 3/195 

Al-Haafiz Ibn Hajar (may Allah have mercy on him) said: 

Ibn Abi Layla is da‘eef. The hadeeth of the door and the one that follows it are indicative of the weakness of what he narrated. End quote. 

Fath al-Baari, 4/252 

Ash-Shawkaani (may Allah have mercy on him) said: 

Its isnaad includes Ibn Abi Layla, who is da‘eef. End quote. 

Nayl al-Awtaar, 4/332 

The scholars differed concerning the reason why the Prophet (blessings and peace of Allah be upon him) fasted most of Sha‘baan and there are many opinions, including the one mentioned above, but the evidence for that is not sound. Perhaps the first one who narrated it was Ibn Battaal in his commentary on Saheeh al-Bukhaari (4/115). He also mentioned other opinions that were narrated by al-Haafiz Ibn Hajar (may Allah have mercy on him) and added to them, then he said: 

More appropriate than that is what is mentioned in a hadeeth that is sounder than what has been mentioned above. It was narrated by an-Nasaa’i and Abu Dawood, and classed as saheeh by Ibn Khuzaymah, from Usaamah ibn Zayd who said: I said: O Messenger of Allah, I have not seen you fasting in any month more than you do in Sha‘baan. He said: “That is a month that people are heedless of, between Rajab and Ramadan, but it is a month in which deeds are taken up to the Lord of the Worlds, and I like my deeds to be taken up when I am fasting.”

End quote from Fath al-Baari, 4/215 

And Allah knows best.