Originally Posted by GrahamL
I would perhaps try closing all the background apps on the 5c (which you can do 3 at a time with iOS 7's new app switcher!) and see if that makes a difference. Multitasking works differently on iOS 7 compared to 6 - you can enable/disable backgroud refresh on a per-app basis, for example. I guess the app used to play the music will make a difference too. I'm using iTunes Home Sharing with the stock music app but that's not to say other apps capable of 24/96 will work properly - which app are you using?
I finally got a chance to try this -- closed all other apps, and then restarted the Music app. Same result. Files that are native 44.1kHz play back cleanly at 44.1kHz, files that are native 48kHz play back cleanly at 48kHz, but files that are native 96kHz play only for a few seconds and then the stuttering starts. This is all with the HRT microStreamer, iPhone 5c, and iTunes Music Sharing using the latest install (11.1) on a Mac.
Now the good news -- inspired by your success, I tried my Fiio E17 through a hub. iTunes streaming allows me to listen to 24/96 files without playback issues. This works on the slower iPhone 4 running iOS7. Audio is clean and clear. Hooray!
That means it is a specific incompatibility with iOS7, 96kHz playback, and the HRT microStreamer. Perhaps it can be fixed with a firmware issue, as HRT were the ones who modified the firmware to make the microStreamer iPad-compatible this past summer. In any event, since this is a pretty special use case for the iPhone for me, I'm pretty happy I can get compatibility for 44.1kHz an 48kHz playback on the microStreamer, and 96kHz playback on the E17.