I wonder if unceasing prayer is to bring up all things before our Triune God as we go through the day. As we think of this or that person, or encounter this or that person, should we not just lift each to God and give them over to our Lord for consideration. Our goal is not to effect our lives or the lives of others, but to be in constant companionship to our Lord Jesus Christ, trusting that he, knowing best for us and others, will effect our lives.