Normally, when your arrow falls off the shelf, it is a result of two things. 1)You aren't using your fingers as a simple hook - keeping the arm relaxed - and drawing with your back muscles or 2) Your hand isn't flat to your face on the draw...alignment issue.
Try 'hooking' your fingers around the string with a ddddeeeeppppp hook (behind or in the finger joint, tips curled back towards your ear) while keeping the wrist flat and forearm relaxed, lining up the shot with bow raised while keeping your head as still as possible, and draw straight back to anchor, using only the back muscles. (Try to pull your elbow behind your head with the back muscles.) If done correctly, the web should come right back and fit snugly around the jaw.
An anchor is NOT the corner of the mouth. That is a 'touch/reference point'...as is any soft tissue contact. An anchor must be a bone on bone contact WHEN the back muscles are fully engaged.
Try anchoring with the web between your thumb and index locked behind the jaw bone and you will see what I mean.