I'm using Ubuntu 12.04 64bit and I'm trying to make a file executable, but when I check the "Allow executing file as program", the check mark appears then disappear spontaneously.
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I know it's an old Q, but still relevant, plus google brought me here (others will come).
The accepted answer is partially correct, by default you can't set executable permissions inside a NTFS or FAT partition (for Ubuntu at least, and up to the date).
But you can change that, by changing the way your NTFS partition gets mounted. That is, (choosing and) configuring the ntfs driver that mounts your partitions.
NTFS supports all permissions you need*, but the driver has to know how to handle them so it doesn't interfere with other OSs.
It's not rocket science, but will force you to understand things you may not care about!
See this (extremely concise) answer to a related question:
*Supports ownership and read/write/execute, for user and group, don't know about setuid or stickybit.