I would agree that the effects of botox slowly wear off. To add a little more information, studies have shown that botox degrades after 90 days. After that time, patients develop different patterns of nerve function return. One group seem to return to full muscle movement quickly, and they often find themselves back in our offices shortly after 3 mos. I have found these patients to be the ones with very active metabolism, ie really stressed, type A personalities, hyper patients, or serious athletes (marathon runners, personal trainers, competetive athletes).
Most patients are not like that, and see a slow return of function that is gradual. Maybe over three more weeks, maybe over three more months. I tell patients to return for reinjection when they feel most comfortable with this process. Some ride it out as long as possible and do botox twice a year. Some, as mentioned above, never want to see movement creap back in, and so reinject every three months.
Regions for botox injection clearly have a threshold dose that must be met, in order to provide the anticipated response. Again, this is established by studies, not just my opinion. Doses above that threshold dose are often encouraged in order to establish a pattern of prolonged effect. More drug means more duration, to a degree. Titrate your dose with your physician.