Why can't the monoidal Dold–Kan correspondence be extended to non-connected CDGAs 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 CDGAs that have the ground field in dim 0 and 0 in negative degrees. It was pointed out by Ben Wieland in the [comments](https://mathoverflow.net/questions/433532/monoidal-dold-kan-correspondence-for-non-connected-cdga#comment1116597_433532) that these algebras should be called connected instead.

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