When Paul says "Pray continually" or in other translations "Pray without ceasing", he is referring to being in a constant communal relationship with God. It is more of an attitude than an action. Paul sees prayer as he sees breathing. We don't stop breathing because if we do, we die. However, breathing for the most part is subconscious. We don't put a lot of thought into each breath, unless we find our self in trouble breathing. The same should be true for our connection and awareness of God in our lives. It should never stop and our attitude should be constant to a point of subconscious. We should merely come to God when we are struggling to breath.
Lord, help me to see my relationship to You as important as every breath I must take.