The Chofetz Chaim says the following story: a girl was walking with a bag of apples when the bag ripped making the apples roll all over. People ran to pick up the apples and the girl just stood there in shock. A man came over to her and said, “Don’t just stand there. Grab as many apples as you can save.

The Chofetz Chaim says the same thing is with our davening. A person might come to Modim in Shemone Esray (near the end of the prayer) and realize he has not concentrated at all. The person might feel like giving up, but the Chofetz Chaim advises that a person should start davening with as much concentration as possible from that point. Grab whatever you can.