They don't stop. The Kepler CCDs read out the signals collected during the accumulated time of 6.02 seconds. The fixed read out time is 0.52 seconds. So each CCD gets one frame every (6.02 + 0.52) = 6.54 seconds. Then Kepler sums up every 9 frames (short cadence) and 270 frames (long cadence). The time between two short cadences is (6.54 x 9) = 58.9 seconds, and (6.54 x 270) = 1766 seconds between two long cadences, but the exposure time is (6.02 x 9) = 54.2 seconds for a short cadence, and (6.02 x 270) = 1625 seconds for a long cadence.
There are totally 95 million pixels available on Kepler CCDs, but the spacecraft can store only 5.4 million. The maximum number of targets is about 170,000. see http://archive.stsci.edu/mast_faq.php?mission=KEPLER