How many podcasts are you downloading....? in an average download session?
Tons of big files?
Also try disabling the System Protection and Intrusion protection modules - if that does not work - turn them both back on and disable the AV module (please make sure not to be downloading email at the same time (Good way to get infected) but then see if acces sis restored..
I have worked heavily with Eeye with itunes issues so list them here - they have been quick to fix them up...
Also are you storing all your downloaded files locally or on a Network storage?
And last - is it just the store that is not coming up or is it timing out on the downloads?