Setup: I have two iOS devices and a Windows PC with iTunes. I am trying to download newly purchased music, book, app, or update an app from the Apple store over my LAN. The LAN has two routers between devices and the internet (D-Link DIR-655 and a Vonage VOIP device). This is the same setup I've had for a few years; I have not changed router configs in that time.
Problem: In the last month or so, the App Store download often fails with various errors (404, 8102, -3150). If I am patient, repeatedly retrying the download eventually resolves the problem, but it can take days of trying, regardless of which device I initiate the download with. This is true when the device is connected to my LAN (be it PC/iTunes with ethernet, or iOS device over wifi).
Research: I have been Googling these errors for a month and they turn up unhelpful advice. Frequently mentioned is disabling Privoxy (which I use, but that would only impact iTunes on my PC, not the mobile devices). Also mentioned, change DNS settings. I have no other connectivity problems so DNS doesn't seem like the cause.
However, if I use cellular connection to install directly to my iOS devices, I have no problem. This leads me to believe there is something about my LAN -- or if something changed in iOS/iTunes that causes intermittent errors.
Question: is there some sort of NAT or proxy setting I need to correct to ensure smooth connections between iOS devices/iTunes and the Apple store?