To repeat the footnote mark is in general not a good idea, because by convention the footnote marks must appear on the same page as the footnote itself. There is no way you can ensure this to happen, because TeX breaks the page where it wants. Endnotes are more appropriate here.
Where repeated footnote marks are often used is inside tables, but there you need a lot of fiddling because the normal footnote mechanism does not work in inner environments such as tables, equations, etc.
Below is an example that will do what you requested. It is the basic mechanism that I have build into the refstyle package.
Please note that a minipage has its own footnote mechanism that is reset every time it is called. Also note that the label must be inside the footnote itself, because it is not visible outside it.
\documentclass{article}
\usepackage{hyperref}
\makeatletter
\newcommand{\reffnmark}[1]{%
\begingroup
\unrestored@protected@xdef\@thefnmark{\ref{#1}}%
\endgroup
\@footnotemark}
\makeatother
\begin{document}
\section{First}
This is a footnote test\footnote{first footnote\label{fn:first}}\par
This is a second footnote test\footnote{second footnote\label{fn:sec}}\par
This is a footnote mark\reffnmark{fn:first} link to footnote~\ref{fn:first}.\par
\fbox{\begin{minipage}{0.5\hsize}
This is a footnote test in a mini page\footnote{first footnote\label{fn:mp}}.\par
This is a footnote mark\reffnmark{fn:mp} link to footnote~\ref{fn:mp}
\end{minipage}}
\end{document}