Hi
There does seem to be a bug here. 
If you stablize a clip and replace the original on the timeline, and then save the project, the reloaded project SHOULD contain the stabized clip.(+any edits/effects etc.) ......IT DOESN'T
NCH should have a look at this.
A workaround is to step along the timeline to the start of the clip in question using the "Go to Next Clip Edge" button under the preview pane and right click the stabilised clip which (correctly) has been added to the media list.
You can now add it to the cursor position on the overlay track. by right clicking it and choosing "Place on Sequence"
(Note: Set the default added media position beforehand in the Options to "Ask Me" otherwise you won't see the options)
Unfortunately any editing you did on the stabilised clip will be lost 
If you haven't done any editing the stabilsed clip will play over the unstabilised clip.
Nat