The problem is that the table is too large even for being contained in a page, so first of all LaTeX pushes it on the next page because it can't be contained in the chapter title.
Then it tries to set it in the next page which again doesn't have room for it, so it pushes it to the next page and finally it gives up.
You simply don't need tabularx.
\documentclass{book}
\usepackage{setspace}
\newcommand{\sym}[2]{%
\noindent
\makebox[4em][l]{$#1$}% <---- adjust to suit
#2\par
}
\onehalfspacing % you seem to be using this (avoid it, if you can)
\begin{document}
\appendix
\chapter{List of Symbols}
\label{ch:AE}
\sym{a}{Semi-major axis of Earth}
\sym{Ant_k}{Antenna number $k$}
\sym{a}{Semi-major axis of Earth}
\sym{Ant_k}{Antenna number $k$}
\sym{a}{Semi-major axis of Earth}
\sym{Ant_k}{Antenna number $k$}
\sym{a}{Semi-major axis of Earth}
\sym{Ant_k}{Antenna number $k$}
\sym{a}{Semi-major axis of Earth}
\sym{Ant_k}{Antenna number $k$}
\sym{a}{Semi-major axis of Earth}
\sym{Ant_k}{Antenna number $k$}
\sym{a}{Semi-major axis of Earth}
\sym{Ant_k}{Antenna number $k$}
\sym{a}{Semi-major axis of Earth}
\sym{Ant_k}{Antenna number $k$}
\sym{a}{Semi-major axis of Earth}
\sym{Ant_k}{Antenna number $k$}
\sym{a}{Semi-major axis of Earth}
\sym{Ant_k}{Antenna number $k$}
\sym{a}{Semi-major axis of Earth}
\sym{Ant_k}{Antenna number $k$}
\sym{a}{Semi-major axis of Earth}
\sym{Ant_k}{Antenna number $k$}
\sym{a}{Semi-major axis of Earth}
\sym{Ant_k}{Antenna number $k$}
\sym{a}{Semi-major axis of Earth}
\sym{Ant_k}{Antenna number $k$}
\sym{a}{Semi-major axis of Earth}
\sym{Ant_k}{Antenna number $k$}
\sym{a}{Semi-major axis of Earth}
\sym{Ant_k}{Antenna number $k$}
\sym{a}{Semi-major axis of Earth}
\sym{Ant_k}{Antenna number $k$}
\sym{a}{Semi-major axis of Earth}
\sym{Ant_k}{Antenna number $k$}
\sym{a}{Semi-major axis of Earth}
\sym{Ant_k}{Antenna number $k$}
\sym{a}{Semi-major axis of Earth}
\sym{Ant_k}{Antenna number $k$}
\sym{a}{Semi-major axis of Earth}
\sym{Ant_k}{Antenna number $k$}
\end{document}

If your descriptions are long and may end up into more than one line, you can modify the definition of \sym to ensure the description is not split across pages:
\documentclass{book}
\usepackage{setspace}
\newcommand{\sym}[2]{%
\noindent
\makebox[4em][l]{$#1$}% <---- adjust to suit
\begin{minipage}[t]{\dimexpr\textwidth-4em\relax}
#2\par\xdef\theprevdepth{\the\prevdepth}
\end{minipage}\par\prevdepth\theprevdepth
}
\onehalfspacing % you seem to be using this (avoid it, if you can)
\begin{document}
\appendix
\chapter{List of Symbols}
\label{ch:AE}
\sym{a}{1 Semi-major axis of Earth}
\sym{Ant_k}{Antenna number $k$}
\sym{a}{2 Semi-major axis of Earth}
\sym{Ant_k}{Antenna number $k$}
\sym{a}{3 Semi-major axis of Earth}
\sym{Ant_k}{Antenna number $k$}
\sym{a}{4 Semi-major axis of Earth}
\sym{Ant_k}{Antenna number $k$}
\sym{a}{5 Semi-major axis of Earth}
\sym{Ant_k}{Antenna number $k$}
\sym{a}{6 Semi-major axis of Earth}
\sym{Ant_k}{Antenna number $k$}
\sym{a}{7 Semi-major axis of Earth}
\sym{Ant_k}{Antenna number $k$}
\sym{a}{8 Semi-major axis of Earth}
\sym{Ant_k}{Antenna number $k$}
\sym{a}{9 Semi-major axis of Earth}
\sym{Ant_k}{Antenna number $k$}
\sym{a}{10 Semi-major axis of Earth}
\sym{Ant_k}{Antenna number $k$}
\sym{a}{11 Semi-major axis of Earth}
\sym{Ant_k}{Antenna number $k$}
\sym{a}{12 Semi-major axis of Earth Semi-major axis of Earth Semi-major axis of Earth
Semi-major axis of Earth Semi-major axis of Earth Semi-major axis of Earth
Semi-major axis of Earth}
\sym{Ant_k}{Antenna number $k$}
\sym{a}{Semi-major axis of Earth}
\sym{Ant_k}{Antenna number $k$}
\sym{a}{Semi-major axis of Earth}
\sym{Ant_k}{Antenna number $k$}
\sym{a}{Semi-major axis of Earth}
\sym{Ant_k}{Antenna number $k$}
\sym{a}{Semi-major axis of Earth}
\sym{Ant_k}{Antenna number $k$}
\sym{a}{Semi-major axis of Earth}
\sym{Ant_k}{Antenna number $k$}
\sym{a}{Semi-major axis of Earth}
\sym{Ant_k}{Antenna number $k$}
\sym{a}{Semi-major axis of Earth}
\sym{Ant_k}{Antenna number $k$}
\sym{a}{Semi-major axis of Earth}
\sym{Ant_k}{Antenna number $k$}
\sym{a}{Semi-major axis of Earth}
\sym{Ant_k}{Antenna number $k$}
\end{document}

\hsizeshould be1.8, not28. – Mico Mar 04 '15 at 23:17tabularxsetup is suspect: the type of the first column (given that you're playing with0.2\hsize) should beX, notl. That way, and with1.8\hsizefor the second column, the second will be 9 times as wide as the first, with the entire table taking up\textwidth. The[H]stuff does nothing useful, by the way -- or is it supposed to be part of the very first cell (in which place its location is very confusing)? – Mico Mar 04 '15 at 23:22[H]is text data in the first cell of the table in your source, that's why it is typeset that way. – David Carlisle Mar 04 '15 at 23:31\hsizeis possible and you have multiplied it by 28! (setting\hsizein anlcolumn has no effect at all as there is no line breaking inlcolumns) – David Carlisle Mar 04 '15 at 23:39tabularxin the way you're using it, even if you loadltablex, is completely wrong.longtableis the right way here. – karlkoeller Mar 06 '15 at 17:33