I can't really give minimal repro for this, so apologies if the question is deemed too localized. I don't have a WP device, but when using Browsertack with any Lumia, this page enters an infinite reload loop.
This neither happens on desktop browsers (including IE), nor on other mobile browsers. I can't see if the issue is localized to WP, or if it's a bug in emulator. This doesn't happen in desktop IE's “emulating” mode either.
What could be causing this?
The problem was due to Windows Phone 8.1 user agent change that now includes Android 4.0. This caused a false negative in Modernizr's History API support check, which in turn caused react-router to use window.location instead of pushstate, and refresh the page on every replaceWith call.