I'm seeing the same problem 4 years later!!! ESRI?
Per Esri Tech support:
NIM039789 -> Labels are disappearing when using the pen tool or the highlighter tool (Markup Toolbar) in ArcReader.
The following workaround is available for this issue:
Prior to publishing the map, set the Label Weight Ranking to "None". Go to ArcMap > View > Toolbars > Labeling and within the Labeling Toolbar select the Label Weight Ranking button > Set the default layer feature weight to "None" > Apply > OK. Republish the .pmf file.
Workaround worked very well.