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). 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 that these algebras should be called connected instead.