Why does my forehead Botox last only 1 month?

Sorry to hear you haven't been happy with the result of your Botox injections.  There are many variables as to why some people don't have as long-lasting resulting.  Your doctor may not have used as much product as necessary to treat your particular concern, some people who are very active metabolize Botox differently than others, and if you have had Botox frequently, sometimes you can begin to see diminishing results.  Let your doctor know about your concerns.  It is realistic to expect that Botox will last from 3-4 months, and I suspect that your physician will want you to be satisfied.  You might also want to consider switching to Dysport or Xeomin, which are similar products but may work better for you.  Best of luck.  

Sometimes foreheads have to be treated very lightly to avoid droopy brows from occurring.  The lighter the dose, the less time it will last.  In my Orange County office, we customize all Botox doses so if they don't last long enough we usually can gradually increase the dose until we find that "sweet spot" between lasting longer and not looking frozen or dropping the brows.