The duration or longevity of Botox or fillers is not at all impacted by weight loss supplements. However, if you lose weight, you often lose it first in the face (yes, totally unfair), and so you may require more fillers after weight loss.
Supplements will have no affect on the longevity of Botox or fillers. Weight loss, especially if you lose weight in your face, will have the effect of requiring more fillers. You may think that your filler did not last as long but the result is really that you lost weight and require more filler to replace the lost volume.