Why can I not reject the exclusion of a partition in Time Machine? I have a MacBook Air 11-inch Mid-2012 running OS X 10.8.2. I have an external hard drive connected via USB. The hard drive has two partitions: an HFS+ partition that I use for Time Machine and a NTFS partition that I use for storing large files that I don't want on my small internal hard drive.

(Side Note: I use NTFS because the drive may need to be shared directly with Windows machines at some point in the future as hardware comes and goes through my hands a lot. I use Tuxera NTFS to write to the NTFS partition with great success so far.)

When I open Time Machine, I see that the data storage partition is in the exclusion list (that partition is named "EXTERNAL"):



When I select the "EXTERNAL" partition and remove it from the exclusion list, there are no errors and the partition is gone. Also, I see that the estimated backup size has increased by the amount of used space on the "EXTERNAL" partition:



However after I click save and then open the "Options..." window again, I see that the "EXTERNAL" partition is still in the list of excluded partitions, exactly like in the first image.

Why can I not back this partition up with Time Machine? I have seen other Mac Users report that that they can backup one partition of a disk to another partition on the same disk, but it does not appear that I can. (My reasoning for doing this is that I'd like the local version control that Time Machine offers for quick restoration of accidentally deleted or modified files. I backup both the internal SSD as well as the "EXTERNAL" partition using CrashPlan for offsite data protection in the case of a full disk failure.)
The problem is that Time Machine is designed for HFS+ formatted volumes.

You might have luck with the Paragon NTFS driver but if the NTFS volume is case-sensitive and your normal mac partition is not, you will have problems backing both up to the same Time Machine volume.

You might be able to use Carbon Copy Cloner to copy the contents of the NTFS volume to an image file but not a bootable one.

Also check out this blog which talks about related NTFS issues.