I think we frequently don't ask enough of God for 2 reasons. We don't have a high enough view of God. We don't realize how powerfully awesome He is, so we don't ask the big things because we don't have faith that he can accomplish them. We also don't trust his love and feel like we are interrupting him or causing him too much inconvenience. If we only realized how much He loves us, we would know that there is nothing He wants more than for us to ask for his help and if we only realized how powerful He is (able to speak time, space, matter, energy, and the whole universe into existence) and that He is not limited by time, then we would not doubt that he "can" or "has time to" do what we ask.
The only thing I would add is to ask for help with situations rather than ask for the solution because God's solutions are better than what we can imagine. It is also good to say and mean what Christ said right before the cross "not my will, but thine be done"