It sounds like what you are describing is having placed labels in the layout view and so when you pan the map in the map frame the labels no-longer represent spatially where they were placed. they now appear to be placed elsewhere?
To avoid this if placing labels I would place therm within the map frame, or create features in a feature class or create them as annotations.
Converting to annotation should be possible and should make them maintain their spatial reference so long as you select the correct map frame to place them into.
If you wanted to go a step further you could convert the annotations to points then label dynamically from points, depending on what you need to accomplish and what your work flow is.
It might be easier to just create a new annotation feature class and manually place the label annotations where you want them.
