Time Machine keeps excluding my hard drive
Why it was possible is strange in the first place. The change may caused by a decision of Apple, packed in an update.

Reformat the NTFS partition to HFS+, will include your drive in Time Machine.

Note: also FAT formatted drives will not be backed up by Time Machine.

Update: Time Machine offers to use an NTFS volume if a write-enabled driver for NTFS is installed before a physical disk with NTFS is introduced to OS X. [source: Enabling Time Machine for a USB HDD with NTFS