The breath does not stop. What happens is the breath stops being an object of awareness because the breath calms but the mind remains too coarse or gross to be aware of the breath. 

Here, the mind must let go more & be more quiet, until the mind can feel the breath again. 

Trying to focus will not help because it is the very act of trying (to focus) that makes the mind too coarse or gross to know the breathing. 

The *supramundane* path of the Buddha is only about letting go. 

The Buddha taught *supramundane* meditation (*jhana*) is developed by making letting go (*vossagga*) the meditation object (<a href="http://www.accesstoinsight.org/tipitaka/sn/sn48/sn48.010.than.html">SN 48.10</a>; end of MN 118). 

> *And what is the faculty of concentration? There is the case where a monk, a disciple of the noble ones, making it his object to let go (vossagga),
> attains concentration, attains singleness of mind. SN 48.10*
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> *There is the case where a monk develops mindfulness as a factor for awakening dependent on seclusion, dependent on dispassion, dependent
> on cessation, resulting in relinquishment (vossagga). MN 118*