It would help if you would post photos of the broken stitches on your quilt.
Is it the piecing stitches that broke? Or the quilting stitches? A lot depends on how the piecing was done (single thread, double thread, how big the stitches are) and/or on how the quilting was done (single thread, double thread, how far apart the quilting lines are, what batting was used). It depends also on what kind of use the quilt got.
Are you wanting to hand quilt your sister's top? If so, it should hold up fine if you (1) choose an appropriate batting, and (2) do the quilting sufficiently close together. The more quilting there is, the less stress is placed on the piecing threads and on the quilting threads over time and when the quilt is washed.
One common cause of stitches breaking is washing a quilt and then hanging it on a clothesline. Water is *very* heavy and places a lot of extra stress on stitches; hanging the quilt over a clothesline places all of that water weight on the few stitches near the top of the hanging. Top-loading washing machines with agitators are also hard on the stitching. A quilt pieced and quilted by hand normally will not have many (if any) broken stitches if the quilting lines are not too far apart and if the quilt is handled appropriately when washing.