I'm not sure why clavicle piercings have such a high rejection rate; maybe it's because of the body's natural movement in this area and/or the flexibility of the skin. For whatever reason, very few of them ever heal completely. Even Madison Stone herself lost the piercing many years ago, and hasn't bothered to have it pierced again.
A "true" Madison is horizontal, adorned with a small curved barbell, surface bar, CBR, or circular barbell. However, anything but a surface bar puts more tension on the ends of the fistula, giving it an even greater chance at rejection. Directional variations, such as a vertical Madison, can also be done and may actually reduce the odds of rejection, especially if it's pierced by an experienced surface piercing artist and uses a surface bar for jewelry. If you want the best odds at not losing your Madison, that's what I'd recommend.
Healing time for this particular piercing can take months, or it may never heal at all. Pay close attention to your aftercare instructions and cross your fingers. Do not hang anything from your piercing; not even small charms. If you're one of the lucky few, you might get to keep your Madison for many years. If not, at least you can enjoy it for a while.