The way I've gotten around it is to launch FIFA with Action closed. Once you're in the menus, minimize FIFA, launch Action, and then return to FIFA. You should be good for the rest of the time. I had this problem a while back and I've been able to record dozens of videos in FIFA since doing this.

A way to work around it: It's a little wonky, but record your gameplay using the video recorder. Use the function "do not record microphone" with this one. While recording gameplay (hotkey F9), hit F10 to record audio-only track. You'll want to make sure in the settings that it is set to a 0-100 mix...