Hi Leonard, there you're seeing the "History update" function in action.

History updating is a mechanism where some objects remember what objects were input into the command that created them, and then when those input objects are edited the command is automatically re-run to recalculate a new updated result.

So in this case here when you move the plane you are triggering a history update and the projection is getting calculated again, and if the projection then completely misses the moved plane that is what will make those objects disappear.

Sometimes this history update mechanism can be kind of confusing when it kicks in when you were not aware of it being set up, maybe it should be off by default for Project instead of on by default.

But you can turn it on or off yourself by selecting the curves that are getting updated (the ones that are disappearing), and then run the Edit > History command and click the "Disable update" button. That will disable history updating for those curves and then they will no longer get recalculated when you edit the objects that were used as inputs into the projection.

- Michael