When an old battlefield is being excavated there will usually be some remains like the weapons of fallen soldiers. However as you note, sometimes thousands of people died in these battles and you won't find nearly that many swords, helmets etc. Where did they go? Mostly looted by the victors. Soldiers were usually poorly paid if paid at all. So, to make soldiering more appealing, they were allowed to loot the battlefield. The choicest loot (slaves, gold, silver) was taken by the commanders, and common soldiers may have had to settle for something less, like some swords or a nice helmet or breastplate. Consequently, by the time everyone was done the bodies of the fallen would have been stripped clean of anything remotely valuable (ie. anything metal). The things that often show up when battles are being excavated are things that were overlooked or no one bothered to pick up - things like arrows and spears (leaving behind arrowheads and spearheads).

For an example, take a look at this: http://gladius.revistas.csic.es/index.php/gladius/article/viewFile/226/228

As has been mentioned by other posters, much of the organic material of ancient weapons (wood, leather, various twines) deteriorates and thus does not survive. Finding organic material is rare, and is usually restricted to places where the natural environment best preserves them. A rather remarkable [Roman shield] (http://s3.amazonaws.com/presspublisher-do/upload/2697/duraeuropos6.jpg) from the late third century A.D. was found in Dura Europos in the early twentieth century, the dry climate of the Syrian desert preserving both it's form and exterior decorations.