Are you running the check on the FrameMaker document itself or on an output document? Do you get any specific information on what is actually wrong with the tables?
The check is done on the output document - a PDF.
The Summary error that results:
Table summaries are optional, but can improve accessibility.
I can correct the errors in the PDF, but I would prefer to address the issue in the source, and resolve it once and for all instead of having to correct it in the PDF over and over.