I just had an "endoscopic brow lift" 8 days ago and my eyelids won't stay closed when I try to sleep. Is this normal?

Typically are a private function may diminish slightly during the healing process. This usually do the swelling of the muscles that affect that eyelid closure. This will resolve in time. It may take 6 to 8 weeks to do so. If you're having severe symptoms you may use ointment and tape the lid shut at night. Good luck. 

Your situation is not uncommon with a prior blepharoplasty especially if the prior surgery was aggressively done. Most probably, there still swelling of the forehead from the endobrowlift and this makes eyelid closure temporarily more difficult. Protect your eyes with artificial tears and nighttime ointment and time should work this problem out for you. Make sure your surgeon knows about this problem.

In the early stages after a browlift, the brow can be quite elevated.  This will pull the lids up, especially if you have had a previous blepharoplasty.  As the swelling resolves the lids will fall into their normal position and you should be able to close normally at night.  For now get some artificial tear ointment and put this into the eyes before you go to sleep to prevent dryness.  

Raising the eyebrows does affect the upper eyelids, so any sort of brow lift can keep the eyelids from closing completely.  Normally, this is just a temporary issue and resolves as the healing process occurs.  Since your endoscopic brow lift was only 8 days ago, there still would be some expected swelling and normally, the brows do drop a bit as they relax after surgery.  If you haven't already, I would mention the inability to close your eyes while sleeping to your surgeon.  There are some measures that should be taken to protect your eyes until you regain complete eye closure again.  

If your eyelids do not close after surgery, you have to return to your doctor immediately to determinewhat steps should be take to protect your eyes from drying out or injury while trying to sleep.It is likely that the problem will resolve, but the eye damage should be avoided until they close.

Best to see your surgeon to discuss your exposed eye lid issues. Over the internet can not offer ant advise.. Good Luck... 

Endoscopic
brow lifts are performed to raise the position of your eyebrows, restoring them
back to their normal or natural position.
During the early post-op period full eyelid closure may not occur during
sleep due to swelling. You should alert your Surgeon, as you may need ointments
or eye drops to help during the healing phase.