Multiple copies of short page on one sheet of paper

I do not know an fully automatically way, but it is possible to do it manually with minimal adjustments.

First way:

Reduce the height of the page to the minimal height by replacing a4paper with pagewidth=21cm,pageheight=4cm (here 21cm is the A4 width and 4cm depends on the text content and margin requirements).

\usepackage[top=2cm,hmargin=2.2cm,paperwidth=21cm,paperheight=4cm]{geometry}

Then create a second small LaTeX document which includes the PDF of the first using the pdfpages pages and places it multiple times on one page:

\documentclass[a4paper]{article}
\usepackage{pdfpages}
\begin{document}
\includepdf[page={1,1,1,1,1,1,1},nup=1x7]{mainfile}
\end{document}

This places the first document (called mainfile.tex/.pdf here) seven times on page. Adjust both the number of 1, and the number of nup=1x to the real number which fit on one page.

Example Result:

---

Second way:

You could create the headers using normal text instead so it can be repeated over the page. A tabular would be adequate here. Putting the main text into one multi-column cell also prevents page breaks inside the text. The the text could be repeated using a loop. Adjust the \vspaces and the repeat numbers to fit your requirements.

\documentclass[a4paper, 12pt]{article}
\usepackage[T1]{fontenc}
\usepackage[utf8]{inputenc}
\usepackage[pdftex]{graphicx}
\usepackage[top=2cm,hmargin=2.2cm]{geometry}
\pagestyle{empty}

\begin{document}

\newcount\num
\loop\ifnum\num<7
\par\noindent
\begin{tabular}{@{}l@{}r@{}}
    \small \today & header \\
    \hline\noalign{\vspace{.5cm}}
    \multicolumn{2}{@{}p{\linewidth}@{}}{%
\hspace*{\parindent}% if par indent is required
 short text  short text  short text short text  short
text  short text  short text  short text  short text  short
text  short text short text  short text  short text  short
text short text  short text  short text  short text  short
text  short text  short text  short text  short text end of the text
}
\end{tabular}
\par\vspace{1cm}%
\advance\num by 1
\repeat

\end{document}