I had this problem with my Bois De Santal Flacon.
I thought i was going to break it trying to twist it out.
I couldn't get it out by hand, so I got one of those rubber pads, no luck.
I was putting a huge amount of pressure pulling up on it,
trying to twist clockwise, then counter, with no avail.
I tried scraping into the crevice between with a pick, nothing there.
I finally tilted the entire flacon upside down, in hope that a little of the juice could work itself into the tight fit between the neck and stopper. I then put lighter pressure pulling up on the stopper, and twisted more lightly counter-clockwise, and held that light pull for a good 15seconds, before the stopper finally budged a tiny bit.
I'm not sure if it was sustained, lighter upward/counter-clockwise pressure....
....or just all that I did cumulatively...
...but i felt so relieved when I did get it open without breaking it.
I was genuinely worried for that 15 minutes, thinking I had a default factice. LOL