Why can't the monoidal Dold--Kan correspondence be extended to non-connected CDGA over a field of characteristic 0? 

I understand that there is a technical problem with the original proof due to Quillen given in ["Rational Homotopy Theory" (Remark on p.223)][1]. However, I don't understand what is the conceptual reason for this.

Edit: In the initial post I mistakenly used the term connective to denote CDGA which have the ground field in dim 0 and 0 in negative degrees. It was pointed out by Ben Weiland in get comments that these algebras should be called connected instead.

  [1]: https://people.math.rochester.edu/faculty/doug/otherpapers/quillen-rational.pdf