Check out the article below to know all the ports that are used by Apple for its services and stores.
Did you have any luck with the above mentioned issue. I have the same issue on my Sonicwall.
My firewall is block all traffic to the Deploy.akamiatechnologies.com which is the apple updates links.
However i did not constitute these changes on the firewall, as it started around the same time as yours.
I had this same issue with my SonicWall today. I fixed it by:
1) Logging into my SonicWall Admin
2) Clicking Security Services
3) Application Control
4) Scroll down mid-page to the drop box under 'App Control Advanced', labeled 'View Style - Category'
5) Drill into that drop box, and select 'Multimedia'
6) You will now see an alphabetical listing of known applications
7) Scroll till you see Apple iTunes, then click the configure link to the right of Apple iTunes
8) A pop-up window will appear with the advanced options for said App
9) The 3rd option down labeled 'BLOCK', drill into that drop down box and select 'DISABLE'
10) Click Ok
11) Do this for the other Apple Apps that you frequently use
Following these steps solved my problem today. After monkeying around with port setups for a substantial amount of time, I decided there had to be an easier way. And sure enough, there was. I hope it works for you too.