I have an unrecovered cost basis for an annuity. It seems that I cannot deduct this from my tax liability if the annuity was created after 1986. Is this true?

The IRS requires the General Rule to be used for annuities starting before July 2, 1986 and the Three-Year Rule was not used.  If the Three-Year Rule was used, the payments are now generally fully taxable.  The General Rule in TurboTax requires you to calculate the taxable amount yourself, then simply enter the result, so select the General Rule.  TurboTax does not do the calculation for you.

Please see this thread of comments  @ Annuity