Maya's a programme that will eat up any system resource if you give it half a chance. Are you on 32 bit or 64? Just that if Maya crashes in a render it usualy that I've hit the Max RAM for a 32 bit system, which I then just get a straight crash.
You can also lower the RAM requirements by making maya write the textures to HDD rarther than hold it in the RAM when rendering by going to the file nodes of the textures and checking use cache.
"No pressure, no diamonds" Thomas Carlyle