I think it's just another bit of Symantec's Security Suite that needs to update itself via the Internet. Before you allow it though I'd like to check further and the answers to the following would help me.
- When you say you've denied it so far how long has it been asking for access? If it's only just started recently it is remotely possible that something has got into your computer and is pretending to be part of the Symantec program.
- Does everything else still run OK or have you noticed any programs running more slowly than normal?
- Does Internet Explorer take a long time to load or shutdown?
- Does Zone Alarm give you the name of the file - something.exe or something.dll? If so could you let me know the exact filename please?