I get the gist of what you're saying Veteran, but I don't view the OP's question in that manner.
My prayer is anemic. I struggle with remembering to do it beyond a haphazard silent prayer prior to falling asleep. I've had my moments and connections with God where I all but felt his presence, but I tend to simply forget and try to deal with the situation myself. Prayer becomes an afterthought. Sometimes I even find myself praying after the event has happened for the event to be different or changed if that makes sense. The cynic in me wants to deride that, but I believe God listens to those.
In regards to the above (from Veteran's post), I'd hazard to say it's not so much about seeing the prayer part as it is how we function in life. I think you can tell the difference of a strong-in-prayer person by how they handle things. They aren't rattled when crazy stuff we call life happens and there is the sense about them - I believe testifying of the Holy Spirit. Prayer takes patience. It takes total acknowledgement that you may or may not be able to do something about what you're praying about, but it acknowledges a total reliance and focus on God.
I'm often reminded of Paul's use of the term mystery when I hear these verses:
Romans 8:26-27
Likewise the Spirit helps us in our weakness. For we do not know what to pray for as we ought, but the Spirit himself intercedes for us with groanings too deep for words. And he who searches hearts knows what is the mind of the Spirit, because the Spirit intercedes for the saints according to the will of God.
I do think we can pray without exactly tending to based on that statement. The Apostle Paul refers to praying without ceasing for various peoples and churches. I don't believe that Paul jumped into a closet for 24-48 hours and prayed on his knees. I think most of the time we wouldn't know he was praying by expressions, postures, and activities so much as we would know he was praying by his confidence. Think about what he went through and how that confidence (which we sometimes all feel borders on arrogance) rests upon him. That, to me, is the Holy Spirit and our guide to be in tune with God in life.
I'm nowhere near that standard. In some ways, I'm getting better, but it's a long road and one that I will continue to struggle with.