Could our impatience have something to do with underlying unbelief... Like "Hurry up God, because I'm really afraid You won't answer the way I want You to."
I heard someone say once we should be in a state of "active waiting", meaning being busy about other things, not focused on the thing we are waiting for. Rest implies that we are not anxious, but at peace.
If I have truly given my request to God, asked in faith, then when ever I think of that particular request, I can say a profound "Thank You" and go on with other things.
The stress and anxiety comes when we focus on "the snaswer" instead of the God who will bring the answer.