I just ran the following test using windows 7 and FMPA 13.0v5:
I Placed a portal on top of the tab panel on a copy of an existing layout.
I resized the portal to make it wide enough to add another field.
I selected a field and used ctrl-D to duplicate it, then used specify fields to specify it as another field. I then very carefully positioned the new field to make sure that it was within the boundaries of the portal row using the mouse and arrow keys. I avoided using the alignment controls in the Inspector. I doubled checked my changes by moving the portal a few pixels to make sure that the field moved when I moved the portal that enclosed it.
I then entered browse mode and the field did not disappear.
There's a known issue caused by using the alignment tools to position the field. If the field is not located within the portal row and you use the align tools to pull it into the portal row, the field does not end up "owned" by the portal row. But that shouldn't result in the field dropping to the background behind the tab control. But the same rules apply to the tab control so if your copied field does not get placed within the tab control when you copy it, you could get those results...