Looks like line-number referencing is broken when using subsequent minipages. MWE follows:
\documentclass[a4paper, 12pt, ]{article}
\usepackage[T1]{fontenc}
\usepackage[italian]{babel}
\usepackage[utf8]{inputenx}
\usepackage{eledform}
\footparagraph{A}
\manuscript{A,B,C,D,K}
\omittext{\textit{om.}}
\varseparator{;\space} % Separator between variants
\parafootsep{$||$ }
\manvarseparator{ $\rightarrow$ } % Separator between manuscrit and variant
\begin{document}
\begin{center}
\begin{minipage}{0.75\textwidth}
\beginnumbering
\pstart
Lorem ipsum dolor sit amet, con sectetuer adipiscing elit. Ut purus elit, vestibulum ut, placerat ac, adipiscing vitae, felis. Curabitur dictum gravida mauris. Nam arcu libero, nonummy eget, consectetuer id, \var{vulputate}{A,C}{{B}{vulptate},{D,K}{vuluptate}} something
\pend
\endnumbering
\end{minipage}
\end{center}
\begin{center}
\begin{minipage}{0.75\textwidth}
\beginnumbering
\pstart
Lorem ipsum dolor sit amet, con sectetuer adipiscing elit. Ut purus elit, vestibulum ut, placerat ac, adipiscing vitae, felis. Curabitur dictum gravida mauris. Nam arcu libero, nonummy eget, consectetuer id, \var{vulputate}{A,C}{{B}{vulptate},{D,K}{vuluptate}} something
\pend
\endnumbering
\end{minipage}
\end{center}
\end{document}