What kind of thread are you using?
I use Bottom Line, which is polyester. Do not believe those old yarns that some will spin about poly cutting fabric - it won't. And it's stronger than cotton thread and won't break.
As Tartan said, there are videos on YouTube that show you how to tie a quilter's knot, and how to thread the needle in a manner that it won't come unthreaded. I made such a video showing both tricks but unfortunately I'm not allowed to post it here.
Also, another tip - DON'T press your binding in half before sewing it onto the quilt. I quit doing that a long time ago and my bindings look and feel much, much better.