As from glossaries v4.24 (2016-05-27), you can use
\GlsSetWriteIstHook{\write\glswrite{page_precedence "rnR"}}
before \makeglossaries:
\documentclass{article}
\usepackage[acronym,shortcuts,toc,hyperfirst=true,numberedsection=nolabel]{glossaries}
\setacronymstyle{long-short}
\GlsSetWriteIstHook{\write\glswrite{page_precedence "rnR"}}
\makeglossaries
\newacronym{ABC}{ABC}{a blue cherry}
\newacronym{DEF}{DEF}{dry eggplant fruit}
\newacronym{GHI}{GHI}{green humongous iceberg lettuce}
\newacronym{JKL}{JKL}{jelly kiwi lentils}
\begin{document}
\pagenumbering{roman}
Today, I ate not only \ac{ABC}, but also \acp{DEF}.
\clearpage
\pagenumbering{arabic}
\Ac{ABC} is sweeter than a \ac{DEF}. And I ate a bit of \ac{GHI}.
The only thing I did not eat were \ac{JKL}.
\clearpage
\pagenumbering{Roman}
~
\clearpage
\ac{JKL} are even worse than \acp{DEF}.
\clearpage
\printglossary[type=\acronymtype,title={List of Abbreviations}]
\end{document}
However, this requires you to know the page ordering in your document. If you want to work it out on the fly, it's possible to adjust the behaviour of \pagenumbering and build a list of the ordering. Since the ist file is generated by \makeglossaries, which is a preamble-only command, the information either has to be saved in an external file and read in on the next run or the creation of the ist file needs to be deferred until the end of the document.
Here's an example of the first approach, which creates a temporary file with the extension .tmp. (The .aux file can't be used in this case, as it's not read until the start of the document.)
% arara: pdflatex
% arara: pdflatex
% arara: makeglossaries
% arara: pdflatex
\documentclass{article}
\usepackage{etoolbox}
\usepackage[acronym,shortcuts,toc,hyperfirst=true,numberedsection=nolabel]{glossaries}
\setacronymstyle{long-short}
\def\pageordering{rnaRA}% makeindex's default
\InputIfFileExists{\jobname.tmp}
{%
\GlsSetWriteIstHook{\write\glswrite{page_precedence "\pageordering"}}
}
{%
}
\def\thispageordering{}%
\newwrite\tmpfile
\openout\tmpfile=\jobname.tmp
\AtEndDocument{%
\immediate\write\tmpfile{\string\def\string\pageordering{\thispageordering}}
\closeout\tmpfile
}
\let\orgpagenumbering\pagenumbering
\renewcommand{\pagenumbering}[1]{%
\orgpagenumbering{#1}%
\ifstrequal{#1}{arabic}%
{%
\appto\thispageordering{n}%
}%
{%
\addpageordering#1\endaddpageordering
}%
}
\def\addpageordering#1#2\endaddpageordering{%
\appto\thispageordering{#1}%
}
\makeglossaries
\newacronym{ABC}{ABC}{a blue cherry}
\newacronym{DEF}{DEF}{dry eggplant fruit}
\newacronym{GHI}{GHI}{green humongous iceberg lettuce}
\newacronym{JKL}{JKL}{jelly kiwi lentils}
\begin{document}
\pagenumbering{roman}
Today, I ate not only \ac{ABC}, but also \acp{DEF}.
\clearpage
\pagenumbering{arabic}
\Ac{ABC} is sweeter than a \ac{DEF}. And I ate a bit of \ac{GHI}.
The only thing I did not eat were \ac{JKL}.
\clearpage
\pagenumbering{Roman}
~
\clearpage
\ac{JKL} are even worse than \acp{DEF}.
\clearpage
\printglossary[type=\acronymtype,title={List of Abbreviations}]
\end{document}
This requires two LaTeX runs before makeindex can be run.
Now for the second approach. To do this, first prevent \makeglossaries from writing the ist file using \noist. Since \writeist and \GlsSetWriteIstHook are preamble only commands, their original definitions need to be saved before they're disabled.
% arara: pdflatex
% arara: makeglossaries
% arara: pdflatex
\documentclass{article}
\usepackage{etoolbox}
\usepackage[acronym,shortcuts,toc,hyperfirst=true,numberedsection=nolabel]{glossaries}
\setacronymstyle{long-short}
\newcommand\pageordering{}
\let\orgwriteist\writeist
\let\orgGlsSetWriteIstHook\GlsSetWriteIstHook
\noist
\AtEndDocument{%
\orgGlsSetWriteIstHook{\write\glswrite{page_precedence "\pageordering"}}
\orgwriteist
}
\let\orgpagenumbering\pagenumbering
\renewcommand{\pagenumbering}[1]{%
\orgpagenumbering{#1}%
\ifstrequal{#1}{arabic}%
{%
\appto\pageordering{n}%
}%
{%
\addpageordering#1\endaddpageordering
}%
}
\def\addpageordering#1#2\endaddpageordering{%
\appto\pageordering{#1}%
}
\makeglossaries
\newacronym{ABC}{ABC}{a blue cherry}
\newacronym{DEF}{DEF}{dry eggplant fruit}
\newacronym{GHI}{GHI}{green humongous iceberg lettuce}
\newacronym{JKL}{JKL}{jelly kiwi lentils}
\begin{document}
\pagenumbering{roman}
Today, I ate not only \ac{ABC}, but also \acp{DEF}.
\clearpage
\pagenumbering{arabic}
\Ac{ABC} is sweeter than a \ac{DEF}. And I ate a bit of \ac{GHI}.
The only thing I did not eat were \ac{JKL}.
\clearpage
\pagenumbering{Roman}
~
\clearpage
\ac{JKL} are even worse than \acp{DEF}.
\clearpage
\printglossary[type=\acronymtype,title={List of Abbreviations}]
\end{document}

makeindexwhich is underlyingglossaries– Mar 29 '16 at 19:00page_precedence = "rnRAa"in amakeindexstyle file – Mar 29 '16 at 19:10xindyto it solves the problem. I didn't know thatmakeindexwas also responsible for the page numbers – riddleculous Mar 29 '16 at 19:10