Perhaps putting the item contents in a \parbox is sufficient.
The \itemsep must also be incorporated in to the \parskip of the box.
\documentclass{article}
\usepackage{enumitem,lipsum}
\newcommand\itemnobreak[1]{\item \parbox[t]{\dimexpr\textwidth-\leftmargin}{%
\parskip=\itemsep\relax#1}}
\begin{document}
\begin{enumerate}
\item \lipsum[1-4]
\itemnobreak{\lipsum[2-3]}
\end{enumerate}
\end{document}

SUPPLEMENT
The OP suggested a useful alternative in a comment, but it needed tweaking to capture the proper behavior of \item and also to allow a \parsep.
\documentclass{article}
\usepackage{enumitem,lipsum}
\newcommand\itemnobreak[1]{\item \parbox[t]{\dimexpr\textwidth-\leftmargin}{%
\parskip=\itemsep\relax#1}}
\newenvironment{block-itemize}{%
\itemize \let\olditem\item \let\closepage\relax \renewcommand\item[1][\relax]{%
\closepage%
\ifx\relax##1\olditem\else\olditem[##1]\fi%
\minipage[t]{\linewidth}\parskip=\parsep\relax%
\let\closepage\endminipage }%
}{%
\closepage \enditemize }
\begin{document}
\noindent\hrulefill
\begin{block-itemize}
\item \lipsum[1-4]
\item \lipsum[2-3]
\end{block-itemize}
\end{document}
\newenvironment{block-itemize}{% \itemize \let\olditem\item \let\closepage\relax \renewcommand\item[1][]{% \closepage\olditem[#1]\minipage[t]{\linewidth}% \let\closepage\endminipage }% }{% \closepage \enditemize }This way, I don't have to remember the open brace and close brace – python152 Feb 21 '19 at 20:53\usepackage[shortlabels]{enumitem}, maybe it has something to do with it? – python152 Feb 21 '19 at 20:56\newenvironment{block-itemize}{% \itemize \let\olditem\item \let\closepage\relax \renewcommand\item[1][\relax]{% \closepage% \ifx\relax##1\olditem\else\olditem[##1]\fi% \minipage[t]{\linewidth}\parskip=\parsep\relax% \let\closepage\endminipage }% }{% \closepage \enditemize }– Steven B. Segletes Feb 21 '19 at 21:17