Preventing Forehead Drooping from Botox?

Botox in the up and down oriented frontalis muscle (forehead) can cause drooping of the brows, since the brow lifting muscle is being deactivated.
Injection of Botox into the crow's feet causes relaxation of the orbicularis, a depressor of the lateral brow. Therefore when the crow's feet are is injected, there is a rise in the lateral brows.
Botox to the frown area doesn't counteract central or lateral brow depression caused by forehead injections, but does give a very slight medial brow lift.

Eyebrow drooping after neuromodulators like Botox, Dysport or Xeomin is a rare but well described issue, usually resulting from product placement or the amount used. 
The first thing that needs to be determined is whether it is a droopy eyebrow or a droopy eyelid. Droopy eyebrows are much more common and result from over-immobilizing the only muscle on the forehead that is able to lift up our eyebrows - choosing the right amount and placement in the right patient is key to good forehead results. Droopy eyelids come from the product getting into the wrong muscle that elevates the eyelid. 
Management of them is quite different, but both have strategies to help expedite resolution while waiting for them to resolve with time, and any experience injector should be very familiar with how to deal with them: drops for the eyelids and precise placement of Botox in the brow depressors when it is an eyebrow issue, which is what you are referring to. 
To ensure you are receiving the highest level of care, seek out a modernly trained, new-school dermatologic surgeon, oculoplastic surgeon, facial plastic surgeon or plastic surgeon who is board certified and fellowship trained in one of these "core four" cosmetic specialties. Membership in organizations like the American Academy of Facial Plastic and Reconstructive Surgery help to identify a highly trained surgeon.
Cameron Chesnut#realself500 Physician

If the frontalis (forehead is injected), and there is laxity of the skin, or you use your frontalis to hold up heavy lids, injecting the procerus (a brow adductor that lowers the central brow with the corrugator muscles between the brows) will lessen the risk of brow drop. In young patients, you can inject the frontalis alone, but older patients will get brow drop if some accomodation not done.

If you have forehead wrinkles, the Botox needs to be placed in the forehead.  If you have glabella wrinkles, the Botox needs to be placed between the brows.  There are ways to minimize the risk of brow drooping.
sek

If you have decreased tone in your forehead skin and you get Botox than it's likely that your brows will drop. In patients like this we tend to stay away from the lateral brows to prevent complete ptosis or sagging. In fact Botox under the lateral brow will paralyze the orbital muscle and slightly raise the lateral brow.
Botox injected between the eye, the glabellar region, will relax the frown lines between the eyes due to paralysis of the corregator muscle. It will do minimal if anything to prevent brow sagging.