Why can I not reject the exclusion of a partition in Time Machine?
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.