Why is the ionization energy of sulfur anion more than that of oxygen anion?
The ionisation energy of an anion is the same as the electron affinity of the element. $$\text{IE}(\ce{A-}) = \text{EA}(\ce{A})$$

Your reasoning is not wrong and one might expect exactly this behaviour. Another point for this reasoning is the substantial lower electronegativity of sulfur ($2.6$) versus oxygen ($3.4$).  However, experimental findings contradict this reasoning.
$$\begin{array}{lll}
&amp;&amp;/\mathrm{kJ\cdot{}mol^{-1}}\\\hline
\text{IE}\ce{(O)}  &amp;        &amp;=1314\\
\text{IE}\ce{(S)}  &amp;        &amp;=1000\\
\text{IE}\ce{(S− )} &amp;=\text{EA}\ce{(S)} &amp;=200\\
\text{IE}\ce{(O− )} &amp;=\text{EA}\ce{(O)} &amp;=141\\\hline
\end{array}$$

Sources: Wikipedia articles on ionisation energies, electron affinities

Basically it all boils down to electron-electron repulsion. Oxygen ($152~\mathrm{pm}$) is much smaller than sulfur ($180~\mathrm{pm}$) (van der Waals radius, source). This goes hand in hand with the smaller orbitals (lower main quantum number for the valence shell)  The electrons can therefore only occupy lesser space and repulse each other more. This is mainly the reason, why sulfur has a greater electron affinity than oxygen.

The same reasoning may be applied to fluorine and chlorine.