Unit root in stationary model

Dear All,
I am coding the flexible prices version of Gertler, Sala and trigari (2008). The model is detrended and log-linearized around the steady state, but I still get an eigenvalue equal to one and so there is a unit-root. The strange thing is that this does not happen in the model with frictions. One thing I have noticed is that the variance of the real prices is really small, but I do not know if that matters.
Could someone help?

Many thanks
mod and ss files.zip (3.02 KB)