Hi Travis,
What format are you trying to output to the deck? You said your footage is 23.98, which is fine, but FCP7 cannot output closed captions on a native 23.98p or pSf signal. FCP7 only supports 1080i 59.94 and 720p 59.94 outputs with closed captions when using the Blackmagic cards.
If you change your Easy Setup to output 1080i 59.94 or 720p 59.94, you can output your 23.98p sequence using telecine (in this case, your caption file should match the output format, not the sequence format).
If this is not your problem (i.e. your Easy Setup/View > Video Playback setting is already set to output 1080i 59.94 or 720p 59.94), you may be experiencing a driver issue that we've gotten a few reports about, so please call me at CPC if you think that might be the case.
Hope this helps,
Jason Livingston
CPC Closed Captioning