First off, I'm using a manufacturer (Apple) refurbished AirPort Time Capsule, the newest model, which was delivered by UPS a few hours ago to my new house. I bought it directly from Apple.
The technician from Hughesnet, which is satellite internet, finished installing the equipment (satellite dish, modem, etc.) earlier today. A tech support rep promised me speeds of at least 9 mbps, with the max being 15. Yet, I'm never able to get more than 7 or 8, nothing close to the already-slow 15 expected or even the 9 that the tech support representative promised.
My problem is that regular webpages (such as Apple, Wikipedia, MLB) all load reasonably quickly, yet I am never able to download iOS 9. After a few minutes, iTunes on my MacBook Pro (mid-2009, running OS X 10.10.5 "Yosemite") will have about "1024.0 KB" downloaded, then the request will time out. The update doesn't seem to be downloading on my iPhone 5S, either, but it downloaded part way on a relative's Wi-Fi network earlier this week.
I've spent literally hours on the phone with Hughesnet's technical support and we were finally able to prove that the modem is working properly and that the problem must be the router.
The Airport Time Capsule has been updated to the latest software. Both the router and the modem have been power cycled multiple times.
Is there something more that I can do to troubleshoot my Airport Time Capsule? Could this just be a problem with Apple's software update servers?
Update: I just ran another speed test using the Ookla Speedtest app and it's now showing a 20 mbps download speed, but the iOS 9 update still won't install.