I would also say that it may be a piecing issue. The max distance apart you can quilt is established by your batting. The packaging will give you this info, but it assumes that the piecing is secure. Before quilting it's a good idea to look over all your seams to ensure that you have a minimum of 1/4". This gives you an opportunity to take a bit larger seam if you find any skimpy ones.
Another thing to consider is the fabric weave. Fabric that has a looser weave, such as homespun or lesser quality quilting cotton can fray or pull apart.
If you piece by machine, you probably won't have an issue, but the seam length normally used is 2.5 or smaller.
These issues can be mitigated by heavier quilting, and if you are worried about a specific seam, then definitely quilt over it. There are some great suggestions above.