Perhaps

Many years after the prophet Alma received a threatening message from an angel and turned his life around, the Lord sent him on a mission to call the Nephites to repentance. As he preached from city to city, he bore his witness of God's reality and of God's desire for the people to repent and turn to Him. Interestingly, he did not speak of his supernatural encounter with an angel as the basis for his faith and testimony. Instead, he spoke of the following conversion process:

Behold, I say unto you they are made known unto me by the Holy Spirit of God. Behold, I have fasted and prayed many days that I might know these things of myself. And now I do know of myself that they are true; for the Lord God hath made them manifest unto me by his Holy Spirit; and this is the spirit of revelation which is in me.
--Alma 5:46

It was not a visit from a heavenly messenger that converted Alma. The angel got Alma's attention, but it was fasting and prayer that brought the change of heart into Alma's life. While the angelic visitation was dramatic, Alma's conversion required diligence and patience. Alma had to wait on the Lord.

Why does God sometimes delay His response to my prayers? Perhaps He is giving me time to prepare for the answer. Perhaps I need the time to hone and refine my request. Perhaps I haven't done all I can on my own yet to truly distinguish between my power and God's power. Perhaps I am not ready to appreciate the answer when it comes. Perhaps I have taken no thought about what I want except to ask. Perhaps the development of patience and endurance are more valuable blessings than the thing I ask for. 

Nevertheless, once I am prepared, specific, and humble, having expended my own best efforts, and learned patience, the answer comes. It may not be what I initially thought I wanted, but it is always what I truly need.