This would better be answered in another Acrobat sub-forum, not Printing and Prepress, but...
Verify a couple things please, or include them in a new post.
This application. Is it a fillable pdf Form?
How was the Form created; in Acrobat via Forms menu or LiveCycle Designer?
How is the user Saving the filled Form; via Save or a Print button?
I would check the properties of the field in question.