Why does chlorination of toluene stop at two chlorine atoms?
It doesn't stop, it just gets a lot slower the more chlorine atoms you add. From the abstract of an article titled Photochemical side-chain chlorination of toluene[1]:


  Where $k_1$, $k_2$, and $k_3$ are the rate consts. for the successive reactions: $\ce{PhMe}$ → $\ce{PhCH2Cl}$ → $\ce{PhCHCl2}$ → $\ce{PhCCl3}$, resp.; $r = \frac{k_1}{k_2}$ and $s = \frac{k_2}{k_3}$, values of $r$ and $s$, resp., were 6.0 and 5.7 at 100° and 8.4 and 8.5 at 40°, for batch operation, with light varying from ultraviolet to yellow.




[1] Haring, I. H. G.; Knol, H. W. Chemical and Process Engineering (London) 1964, 45 (10), 560–567.