This happens because PGFPlots only uses one "stack" per axis: You're stacking the second confidence interval on top of the first. The easiest way to fix this is probably to use the approach described in "Is there an easy way of using line thickness as error indicator in a plot?": After plotting the first confidence interval, stack the upper bound on top again, using stack dir=minus. That way, the stack will be reset to zero, and you can draw the second confidence interval in the same fashion as the first:
\documentclass{standalone}
\usepackage{pgfplots, tikz}
\usepackage{pgfplotstable}
\pgfplotstableread{
temps y_h y_h__inf y_h__sup y_f y_f__inf y_f__sup
1 0.237340 0.135170 0.339511 0.237653 0.135482 0.339823
2 0.561320 0.422007 0.700633 0.165871 0.026558 0.305184
3 0.694760 0.534205 0.855314 0.074856 -0.085698 0.235411
4 0.728306 0.560179 0.896432 0.003361 -0.164765 0.171487
5 0.711710 0.544944 0.878477 -0.044582 -0.211349 0.122184
6 0.671241 0.511191 0.831291 -0.073347 -0.233397 0.086703
7 0.621177 0.471219 0.771135 -0.088418 -0.238376 0.061540
8 0.569354 0.431826 0.706882 -0.094382 -0.231910 0.043146
9 0.519973 0.396571 0.643376 -0.094619 -0.218022 0.028783
10 0.475121 0.366990 0.583251 -0.091467 -0.199598 0.016664
}{\table}
\begin{document}
\begin{tikzpicture}
\begin{axis}
% y_h confidence interval
\addplot [stack plots=y, fill=none, draw=none, forget plot] table [x=temps, y=y_h__inf] {\table} \closedcycle;
\addplot [stack plots=y, fill=gray!50, opacity=0.4, draw opacity=0, area legend] table [x=temps, y expr=\thisrow{y_h__sup}-\thisrow{y_h__inf}] {\table} \closedcycle;
% subtract the upper bound so our stack is back at zero
\addplot [stack plots=y, stack dir=minus, forget plot, draw=none] table [x=temps, y=y_h__sup] {\table};
% y_f confidence interval
\addplot [stack plots=y, fill=none, draw=none, forget plot] table [x=temps, y=y_f__inf] {\table} \closedcycle;
\addplot [stack plots=y, fill=gray!50, opacity=0.4, draw opacity=0, area legend] table [x=temps, y expr=\thisrow{y_f__sup}-\thisrow{y_f__inf}] {\table} \closedcycle;
% the line plots (y_h and y_f)
\addplot [stack plots=false, very thick,smooth,blue] table [x=temps, y=y_h] {\table};
\addplot [stack plots=false, very thick,smooth,blue] table [x=temps, y=y_f] {\table};
\end{axis}
\end{tikzpicture}
\end{document}
Because you gave no complete MWE and you given datas were not complete I had a little bit to guess how your code could look.
Nevertheless the following MWE compiles with a current MiKTeX 2.9 without an error message nor a warning (the shown two warnings throws filecontent I have used to include both csv files to the MWE).
As you can see I changed the dates in your active table. With your original version there are three errors and no pdf (your original file is included, but I commented it. If you want to test, uncoment it and comment the other version).
At last I changed the dates a little bit to get a similar picture you showed.
MWE:
\RequirePackage{filecontents}
\begin{filecontents*}{\jobname-daily.csv}
date,count
2014-11-17,5
2014-11-18,0
2014-11-19,0
2014-11-20,1
\end{filecontents*}
%\begin{filecontents*}{\jobname-active.csv}
%date,active
%Jan 24,49
%Jan 25,46
%Jan 26,44
%Jan 27,47
%\end{filecontents*}
\begin{filecontents*}{\jobname-active.csv}
date,active
2014-11-24,49
2014-11-25,46
2014-11-26,44
2014-11-27,47
\end{filecontents*}
%\documentclass[border=5mm]{standalone}
\documentclass{scrartcl}
\usepackage{graphicx}
\usepackage{pgfplots}
\pgfplotsset{compat=1.12}
%\usepackage{pgfplotstable}
\usepackage{tikz}
\usetikzlibrary{plotmarks,backgrounds,pgfplots.dateplot}%fpu calendar
\begin{document}
\begin{figure}
\centering
\begin{tikzpicture}[tight background, trim axis left]
\begin{axis}[%
date coordinates in=x,
scale only axis,
ytick={0,25,50,75,100},
grid=both,
width=\textwidth,
height=3cm,
xticklabel=\day-\month,
legend pos=north west]
\addplot [color=blue,mark=x]
table [col sep=comma,y=count, x=date] {\jobname-daily.csv};
\addlegendentry{Legend1}
\addplot [color=red,mark=*]
table [col sep=comma,y=active, x=date] {\jobname-active.csv};
\addlegendentry{Legend2}
\node[anchor=west] (source) at (axis cs:2014-11-20,30) {%
Monitoring started};
\node (destination) at (axis cs:2014-11-24,49) {};
\draw[->] (source)--(destination);
\end{axis}
\end{tikzpicture}
\caption[Daily activity of thesystem]{Daily activity of thesystem during the collection time span.}
\label{fig:daily}
\end{figure}
\end{document}
and the result:
Best Answer
Using dashes instead of slashes compile without errors.