The month of Ramadaan is a blessed month, during which the Qur'aan was revealed, and the process of inspiration started upon the Prophet صلى الله عليه وسلم. Therefore, the du'a of Ramadaan is a blessed du'aa', and this can be inferred from the Prophet's hadeeth صلى الله عليه وسلم:
إِذَا دَخَلَ رَمَضَانُ فُتِّحَتْ أَبْوَابُ الجَنَّةِ ، وَغُلِّقَتْ أَبْوَابُ جَهَنَّمَ ، وَسُلْسِلَتِ الشَّيَاطِينُ
"When Ramadaan comes, the Doors of Paradise are opened, and the Doors of Hell are closed, and the Shayaateen are chained up."
So it can be inferred from this hadeeth that du'aa' during Ramadaan has a greater chance of being accepted, as the Gates of Paradise and Mercy are opened.  Notes:
 Reported by al-Bukhaari and Muslim.
 Shaykh Dr. Abu Ammar Yasir Qadhi حفظه الله, Du'a - The Weapon of the Believer, p. 128.
Fasting the Month of Ramadaan