This is a common problem with ANY knitted/stretchy fabric. ZigZag stitch is the commonly suggested solution. Some machines have a built in stretch stitch. You can also try easing up the tension and using a straight stitch so there's a bit of excess thread. When a fabric stretches, you want your stitches to accommodate this.
The quilts that I've seen with minkee piecing it was mixed with quilting cottons which probably stabilized the seams. Haven't seen any all minkee pieced quilts. Bet it's soft!