If there is just some weird connection thing going on, you might be able to work around it.
Re-import the video clip into the same group as current video. Then drag any adjusted parameters (ie: Transform, Blend Modes, etc.) from the broken video onto the newly imported video. You should be able to quickly replace the broken linked video with proper moving video.
On the subject of the problem:
I’ve seen issues like this before. Usually it happens when an FCP project has been media managed and the clips that were sent to Motion have been trimmed. The media start/end times on the trimmed media no longer matches what Motion recalls, so even when you reconnnect the clip, you get a still image instead of moving video. I wonder if that is what happened to you.
Andy