A Muslim must have this thing clear in his or her mind that Allah Almighty is the listener of Duas and He does respond to a person sooner or later. However, there are different person whose dua Allah Almighty never rejects. Most of us make dua after recitation of Quran(http://www.quranreading.com/online-quran-recitation) or after saying prayers. The following hadith of Prophet (PBUH) is very enlightening in this regard:
“There are three persons whose Dua is not rejected, the fasting person until he breaks the fast, the just ruler, the oppressed person are the ones whose Dua Allah Almighty lifts above the clouds and opens unto it the doors of Jannah and Allah says: “I swear by my honor, verily, I shall assist you, even though it may be after sometime.” (Narrated by Abu-huraira)
Therefore, a fasting, oppressed person and a just ruler are the ones whose dua is never rejected by Allah Almighty, however, the response can be delayed as Allah Almighty deems fit.