The reason of the error is that \section only works in vertical mode and \savebox uses restricted horizontal mode. Giving it a width doesn't change that. You could use a minipage environment inside the savebox to have vertical mode internal:
\documentclass{article}
\newsavebox{\meinebox}
\begin{document}
\begin{lrbox}{\meinebox}
\begin{minipage}{\linewidth}
\section{Hier}
\end{minipage}
\end{lrbox}
\noindent\usebox{\meinebox}
A lot of text.
\par\noindent
\usebox{\meinebox}
\end{document}
However this will not lead to the same result as using \section normally, because \usebox forces horizontal mode. Better is to use a vertical savebox, which however isn't provided by LaTeX itself. You need to use TeX primitives for that:
\documentclass{article}
\newsavebox{\meinebox}
\begin{document}
\setbox\meinebox\vbox{%
\section{Hier}
}
\copy\meinebox
A lot of text.
\par
\copy\meinebox
\end{document}
Still, I wouldn't recommend to use boxes at all, but to reset the section counter to the previous value.
\documentclass{article}
\newcounter{mysection}
\begin{document}
\setcounter{mysection}{\value{section}}
\section{Hier}
A lot of text.
\section{Other}
\setcounter{section}{\value{mysection}}
\section{Hier}
\end{document}
Counters are always global with LaTeX, so you need to backup the correct section count if you need it afterwards:
\documentclass{article}
\newcounter{mysection}
\newcounter{mysectionbackup}
\begin{document}
\setcounter{mysection}{\value{section}}
\section{Hier}
A lot of text.
\section{Other}
\setcounter{mysectionbackup}{\value{section}}
\setcounter{section}{\value{mysection}}
\section{Hier}
\setcounter{section}{\value{mysectionbackup}}
\section{Third}
\end{document}
Note that all solutions will cause trouble with section references, hyperlinks and PDF bookmarks because the section counter or its label is used twice.
sections the top-most sectioning division, or do you havechapterand evenpartdivisions? When the section is re-introduced, do you want to re-use the originalchapterandpartnumbers as well, or just the originalsectionnumber? Separately, are you looking to replicate just the section header or the header and the entire contents of the section? – Mico Jan 07 '13 at 21:26