Unless the animation model is extremely heavy, which would drive your ram to oblivion, your machine spec is definitely good enough to handle doing animations.
If you ask me, it sounds like some kind of stupid anomaly in your model, a piece of corrupted geometry perhaps? Try doing some trial and error seperation of your model to weed it out. Other things that can cause rediculous crashes are hardware accelleration and graphics driver issues. This is currently happening to me on an occasional basis and has only started happening with max2010 - i am trying to get to the bottom of it. Make sure you have neatly organised your textures and you dont have any that are a whopping great size in your scene. It sounds daft but sometimes the sheer effort for max to find your resources over a network, or load a huge texture into ram, is enough to crash it.
For what its worth, in my experience when it comes to animation the most important thing (much more so than still images) is to be REALLY organised. Keep everything your model organised and well named, proxy whatever you can our your model, keep your materials, cameras, grouping, references, xrefs, and project folder well named and organised etc. You cannot be too organised when undertaking an animation. That way you know what everything is and where it should go... and you can troubleshoot your project faster if problems arise.
good luck.