All three members of the Godhead are involved in and concerned with our prayers. Each of them stands in his specific and appointed position and performs his designated service for men. Their labors in this respect are identifiable and distinct and must not be confused or misunderstood. The true doctrine of prayer is this: We worship and pray to the Father, in the name of the Son, by the power of the Holy Ghost. This is the one and only approved order; there is no other.
Elder Bruce R. McConkie, "A New Witness for the Articles of Faith"
It takes on a new meaning when you think of the Godhead fulfilling a calling. Each one is doing His role. I always thought that this was God's work and He can do whatever He feels or even delegate it. I don't expect Him to work, right? Afterall, He is the very top of the chain of command, so to speak. At least my head thinks that way.
But....His work is so organized and perfect, that He and the other members of the Godhead have a specific role to do. And... They do it, perfectly.
The Lord says..."ask and ye shall receive". When we ask, each member of the Godhead does His role in answering. They are bound to. They cannot and will not lie. There is no other way of doing this. Now....we may think we are not getting an answer. That's because of two things....one, we just aren't listening. We aren't in the right mindset to hear. And, two, we are expecting the answer to come in a particular manner, therefore, we are too distracted to hear it when it comes in God's way.
Point is, They are answering our prayers. Well, God is... when we ask in the name of His Son, then He answers through the Holy Ghost. They are doing their jobs, for each of us. Now, we may not like the answer or the answer may be..."not right now", but the answer will come. Could come by way of a personal visitation, or an audible response, or via a feeling, or via a thought. All of which is personal revelation. But, to hear the answer, we must be prepared and listening....remember that.