I encountered this problem tonight with a brand new Brother MFC-J6540DW and Adobe Acrobat Pro 2024.001.20604. When I found this thread, my first reaction was: Over five years have passed, and it's still broken. Yuck.
But I was able to solve the problem by selecting a different driver.
My initial failure was with the one named "WIA-Brother MFC-J6540DW (94ddf809.1.0...". (There are more characters in the name, but it's in a list that truncates them and can't be resized.)
I chose "TW-Brother MFC-J6540DW LAN 5.0 (32.32..." and got it to scan multiple pages.
I don't know why Brother's driver installer installs three different drivers or what they're supposed to be for. Only that the first one won't scan a whole file, but the second one will.
If there is more than one driver for your scanner, try different ones.