I figured out that the rules that were placed in this form cause the behavior and they had to remain in place due to requirements. So, I have a solution if anyone else bumps into this problem. I added a new text field and in the properties of the text box I placed the DisplayName of the People Picker as the value. I also checked to Refresh the value when formula is recalculated. This now retains the value I have in the People Picker. Finally, I created a formatting rule to hide the field on a condition.
Sean