I've had the same trouble as the OP since upgrading to iOS 8.4 to try out Apple Music, and tired of reading all these threads telling me to connect my Airport device to a wired network. I've been running music through this Airport Express over my same wifi network for *years* with the rdio app without the cutting in and out problem. iOS 8.4 definitely introduced something that causes the problem because now all music streamed to this Airport Express cuts in and out from any app, including rdio which I didn't have the problem with previously.
Another sign this isn't necessarily the connection and more about the phone - I can recreate cutting in and out just by using the phone normally. i.e. opening apps, using Safari. (I have a 6+ so not an old phone CPU.)