In this instance, straight stitch is better than zigzag. Zigzag stitches are used to allow movement in the fabric. In effect, a poor man's stretch stitch. It has longer segments of thread exposed. The longer the segment, the more likely to break. Having said that, I don't think you need to redo the stitching. You should be fine.
IMO the stitch lines do very little to provide strength. The strength of the piece comes from the durability and strength of the fabric. The stitch lines keep everything in place. Multiple stitch lines provide redundancy so if the closest line fails others are there to keep things in place. In theory, one line is all that is _needed_ but more than one provides backup.
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