I have unused tuition and education amounts from previous years, but they aren't being applied against my return to reduce my tax bill to zero - why not?

If you live in ON you may be subject to the Ontario Health Premium which can not be offset with credits. Review the summary details under the "Provincial" tab. Also review all applicable line items under the detailed federal tax summary.

You can find a detailed summary of your tax return under the "Review" tab > "Bottom Line (tax summaries)"> then look for the paper and magnifying icon in the lower left hand corner, select "Detailed Tax Summary". You will have a line by line sample of the Federal Tax Return. 

This does not solve my problem, unfortunately.

See above update to this answer.

If you still have Provincial Tax payable you will need to confirm the entry for provincial carry forward amounts under the "Deductions" tab > "Students" and Tuition carry forward. You must enter the federal and provincial amounts separately. Then review the Provincial Tax Summary for application of this credit.