Manual solution
An admittedly not very comfortable solution is doing it manually, for example with KOMA-Script's \multiplefootnoteseparator:
\documentclass{scrartcl}
\usepackage{endnotes}
\let\footnote=\endnote
\begin{document}
Comma delineation of consecutive footnotes fails upon conversion to
endnotes\footnote{First note.}\multiplefootnoteseparator\footnote{Second
note.}.
\theendnotes
\end{document}

Or with a standard class something like this:
\documentclass{article}
\newcommand*\multiplefootnoteseparator{%
\textsuperscript{\multfootsep}\nobreak
}
\newcommand*\multfootsep{,}
\usepackage{endnotes}
\let\footnote=\endnote
\begin{document}
Comma delineation of consecutive footnotes fails upon conversion to
endnotes\footnote{First note.}\multiplefootnoteseparator\footnote{Second
note.}.
\theendnotes
\end{document}

The package scrextend may also be loaded to integrate KOMA-Script's \multiplefootnoteseparator in standard classes.
Automatic Solution
My package fnpct offers a different solution. If loaded together with the endnotes “it just works”:
\documentclass{article}
\usepackage{endnotes}
\usepackage{fnpct}
\begin{document}
Comma delineation of consecutive footnotes fails upon conversion to
endnotes\endnote{First note.}\endnote{Second note.}. \theendnotes
\end{document}

fnpct also reverses the fullstop and the footnote markers but that can be changed with a package option.
\documentclass{article}
\usepackage{endnotes}
\let\footnote\endnote
\usepackage{fnpct}
\setfnpct{reverse,before-punct-space=0pt}
\begin{document}
Comma delineation of consecutive footnotes fails upon conversion to
endnotes\footnote{First note.}\footnote{Second note.}.
\theendnotes
\end{document}
