Anorexia and Botox - does Anorexia cause Botox to wear off faster, or is my eating disorder making me age faster somehow?

There’s no scientific correlation between Botox and anorexia affecting the face. You will age faster if you are anorexic, but Botox will not wear off faster because you are anorexic.

The eating disorder is probably making it difficult for your body maintain adequate amounts of collagen and fat in the face and this is results in "deflation" of the face. The smoking is probably not helping either. I think the best thing to do is get help with the eating disorder and start putting on some weight. 

Anorexia and smoking will contribute to significantly to wrinkles.  Botox will help but you could be forming antibodies against the structural products that Botox is manufactured with since you are getting it so often.  These proteins do not do anything to make Botox work faster, better or longer; they are just there.  I'd recommend trying Xeomin, a product that doesn't have any structural proteins associated with it.  I call it "organic Botox" for that reason.   Perhaps it will work better for you.  The best option though is to get the help you need for your eating disorder and STOP SMOKING!  I know its a tell order but it is in the best interest for your health and life (not to mention your wrinkles).