Observation: As the author discusses sacrifices, he calls out the simple fact that the ritual sacrifices of the old law and of the temple did not result in addressing sin. Yes, they were acts of obedience toward the Lord, and were done in a manner to atone for sins. However, they had to be repeated over and over because they didn't stop sin or take it away from a human's heart. In fact, what they really did was remind everyone of their sins, bringing them forefront in one's mind so they would consider what they had done.
This is one of the interesting elements of the law as it was originally taught, and then some of the early Jewish traditions as the established to keep the law. Many of them are acts designed to make individuals think about their sins. From ringing bells, to personal examinations of ceremonial cleanliness, to tassels on shawls, to what cuts of meat to eat for dinner, all of these require a thought process that involves personal examination of a person's behavior.
And yes, while our 'continual' prayers are to include requests for forgiveness of sin, Jesus now removes sin from the lives of believers. We are to be obedient and not sin, but an examination of sin is not necessarily a moment-by-moment activity in our lives. In fact, once forgiven of sin, it is to be forgotten as we are to trust that the Lord - by our faith in Jesus - has actually removed that sin from our record. It isn't covered up by the blood of a goat, rather it is expunged from the book of our life by faith in Jesus, and by his atoning sacrifice.
Application: I am keenly aware of my sins every day, and often feel depressed as I think about past sins. I am reminded to of this fact I know ... faith in Jesus means I'm allowed to forget those past sins and simply live into a future of obedience and joy.
Sure, there is a problem when I fail to reject sin in my life, and especially when I repeat the same sin over and over again. This demonstrates a lack of faith, and a lack of dependence on the Holy Spirit for correction and direction in my life. However, that is very different than spending time in remembrance of past sin, and performing rituals or practices that remind me of my failures. I don't need to be doing that. In fact, I am instructed not to be doing that. I am a new creation, washed clean from my past, and with my feet rewashed regularly when I simply ask for forgiveness.
Prayer: Lord, I do ask for forgiveness of my sins, in the name of Jesus. May I look forward to my actions today, not because I remember my sin and worry about repeating them, but because I have joy in this life and knowledge of how I should obey you, and am delighted to do your will this day. Amen.