I agree. If you did not measure through the middle of the quilt and cut the borders to exact size before sewing them on, that is the problem.
If you did pre-measure, pin, and sew then the edges are getting stretched on the frame. One thing that helps is cutting the borders on the lengthwise grain (parallel to selvedge) as that grain is more stable and stretches less. A lot of quilters also stabilize the edges on a frame before quilting. That is, they sew or baste down the sides after each roll, before quilting.
Another thing you can do is pin the edges on each side before quilting (remove the pins before rolling). Pinning allows you to work in any excess fabric at the edge for each section.