React has fairly good support for most drag/drop scenarios except for the case where the dragged component will change parent elements. In that case, touchmove events will stop firing. Without React you'd normally just do something more imparative and just manually move an object around without destory it. In React you likely rely more on state/props to render your scenes; therefore, things become vaguely intractable. Even if your touchmove events are attached to document.body or window (etc) your touchmove event will still not fire.
I've read some discussions on the matter here:
I recently needed to address this in a codebase I work on. I just wanted to report some findings and success I had working around this particular issue. I found this workaround (and I have no idea why it works) https://stackoverflow.com/questions/33298828/touch-move-event-dont-fire-after-touch-start-target-is-removed