Not typically. The Site is in battle, so if your opponent plays a card that discards all cards in battle (like Deceit of Sapphira) then the Site would be discarded (as Raven instaposted). However, if your opponent plays Christian Martyr on your only hero in battle, your access site is okay. Of course, if the battle was your second with New Jerusalem or Promised Land, then it would be discarded per their SA's.
