Full automation is right now only possible with a code change. As a one-off it is easy: Before the environment set the counter unbalance
to 2. This will enlarge the starting vertical size by 2 \baselineskip
s.
The counter will be reset to zero after each environment.
A more general solution that does it automatically could look like this:
\documentclass{scrartcl}
\usepackage[balancingshow]{multicol}
\parindent 0pt
%-------------------------------------------------------------------------------
\usepackage{regexpatch}
\newcounter{multicolminlines}
\setcounter{multicolminlines}{1}
\makeatletter
\xpatchcmd\balance@columns
{\ifnum\dimen@<\topskip
\mult@info\@ne
{Start value
\the\dimen@ \space ->
\the\topskip \space (corrected)}%
\dimen@\topskip
\fi}
{\skip@\c@multicolminlines\baselineskip
\advance\skip@-\baselineskip
\advance\skip@\topskip
\ifnum\dimen@<\skip@
\mult@info\@ne
{Start value
\the\dimen@ \space ->
\the\skip@ \space (corrected)}%
\dimen@\skip@
\fi
}
{\typeout{Success!}}{\patchFAILED}
\makeatother
%-------------------------------------------------------------------------------
\begin{document}
Some onecolumn text goes here on top of the page \ldots
\setcounter{multicolminlines}{3}
\begin{multicols}{2}
This text is balanced into two columns, although it is very
short. How can I prevent balancing below 3 lines minimum
height?
\end{multicols}
Some more onecolumn text goes here below the twocol part \ldots
\setcounter{multicolminlines}{2}
\begin{multicols}{2}
This text is balanced into two columns, although it is very
short. How can I prevent balancing below 3 lines minimum
height?
\end{multicols}
\begin{multicols}{2}
This text is balanced into two columns, although it is very
short.
\end{multicols}
\setcounter{multicolminlines}{1}
\begin{multicols}{2}
This text is balanced into two columns, although it is very
short.
\end{multicols}
\end{document}
If we apply this patch then we get the following output (note that I change the minimum number of lines for the various environments):
