longtable overwrites page number

Question

In my thesis I need to display a lot of long tables for which I use the longtable environment. Most of the time it works perfectly, but sometimes for some reason it doesn't split the table and the table goes well over bottom margin of the page covering a good part of the footer (sometimes even overwriting the page number).

I tried to construct a minimal working example but didn't really succeed. The best I could do was this:

\documentclass[a4paper]{article}

\usepackage{longtable}

\begin{document}

Minimal working example.

\vskip 14.205cm

\begin{description}

\item one
\item two
\item three
\item four

\end{description}

\begin{center}
\begin{longtable}{l|l|l}
\textbf{$f$-vector} & \textbf{ratio} & \textbf{generating grid point} \\ \hline
\endhead
$(8, 12, 6)$ & $1/2$ & $(0, 0, 0)$ \\
$(12, 18, 8)$ & $1/2$ & $(88/1413, 0, 0)$ \\
$(16, 24, 10)$ & $1/2$ & $(706/1413, 0, 0)$ \\
$(18, 28, 12)$ & $1/2$ & $(21/628, -21/628, 0)$ \\
$(21, 32, 13)$ & $1/2$ & $(2825/5652, -1/5652, 0)$ \\
$(24, 36, 14)$ & $1/2$ & $(1/4, -1/4, 0)$ \\
$(25, 38, 15)$ & $1/2$ & $(313/628, -1/5652, 0)$ \\
$(28, 42, 16)$ & $1/2$ & $(539/5652, -187/5652, 0)$ \\
\end{longtable}
\end{center}

\end{document}

In principle it shows what's wrong. The table should be broken and not continue so far into the footer. That's a least what I would like to have. And as I wrote above, sometimes it even goes over the page number.

Any idea what's wrong and how can I fix it?