Sometimes after you split an audio region into two or more shorter regions, the first part of your new regions won't play back as expected. Specifically, the beginning part may not play back properly or at all if the region's anchor point appears at the very end.
This can happen if you split an audio region at the same point as its anchor. In the example below, our region starts a bit before bar 5 and ends at bar 21 in the Arrange window.
If we look at the region in the Sample Edit window, the anchor for the region appears exactly at bar 5 (the black triangle below the region). We set it this way because the downbeat falls exactly on bar 5 in this audio region (the audio before bar 5 is a pickup).
When we split the region at bar 5 and again at bar 13, our region looks like this in the Arrange window:
When we open the first region—the short one that starts a bit before bar 5—in the Sample Edit window, the anchor still appears at bar 5, but it's now at the very end of the region.
This is the cause of the issue—Logic won't play a region back properly if its anchor is at the very end. To resolve the issue: In the Sample Edit window, choose Edit > Update Arrange Position, then drag the anchor back to the beginning of the region, or to a point before the very end, as in this image: