Mac appstore/iTunes store not connecting

It seems that after the last security update for Mavericks my connection to the appstore doesn't work:

"iTunes could not connect to the iTunes store. The host is down"

...this message is hanging there for a week or so. Can anybody tell me how to deal qith this stupid error?

Thanks!

firedept said:

Try signing out and back in again. This has worked for me. Hopefully it will work for you.

Click to expand...

No, unfortunately that doesn't work.

I tried a lot of what can be found by searching, but alas... This problem seems to exist for years already. Nobody here to help, please?

iTunes 12.1.2.27
OS 10.9.5