Yes, I can access the iTunes store.
I used to have this problem only over my work network. however, now, after having changed my home network to a new provider with Wi-Fi access, I can no longer access the iPhone wirelessly through iTunes. The only way to sync it at home or through work is through connecting the phone with the cable. Once the cable is unplugged, the phone disappears from iTunes, even when both the phone and the laptop are connected to the same network.
What could be the problem?