This is probably happening during sync. Go into your Android sync settings and choose "Sync now" in the Google section. The "Request permission" message should pop up.
This appears to often be connected with the My Tracks application. If you are using it, go into the My Tracks settings and turn off the synch. Make sure to do it in the app, not the Android settings. After that, "Sync now" should no longer bring up the message. Now turn the sync back on in the My Tracks settings. It should ask you for an additional permission. Allow it and the problem will be fixed.
If you are not using My Tracks, maybe you will find a similar issue with another application. However, in every case I've heard of lately where the app was identified, it turned out to be My Tracks. That's what it was in my case as well.