Praise be to Allaah.
Abu Dawood (3237), al-Tirmidhi (738) and Ibn Naajah (1651) narrated from Abu Hurayrah (may Allaah be pleased with him) that the Messenger of Allaah (peace and blessings of Allaah be upon him) said: "When Sha'baan is half over, do not fast." Classed as saheeh by al-Albaani in Saheeh al-Tirmidhi, 590.
This hadeeth indicates that it is not allowed to fast after halfway through Sha'baan, i.e., starting from the sixteenth day of the month.