The above mentioned factors that Islam pointed out are important in the duration of botulinum toxin. The reason that the effect of botox wears off in that amount of time is because the presynaptic terminals recover function.
However, there is some findings that suggest Zytase (zinc and the enzyme phytase) can prolong the life of Botox. This is because zinc is required for botox to work effectively. After all, Botulinum toxin A is zinc matrix metalloprotease. Below is a paper about the study that showed the efficacy of zinc/phytase supplementation.