For some big sites, 35,000 products & 500,000 SKUs for example, the speed at which pages are served begins to slow down after the var/cache directory fills up.
The problem can be resolved by switching Magento's backend default filesystem cache (in var/cache) to an in-memory cache directory using Redis or Memcached.
If this problem persists, try flushing both the Magento cache and Redis/Memcached manually.