Addressing subforms takes another level of object reference.  As written,
this version trying to requery the subform control on the main form.

   [Forms]![frmPerson]![sfrmEmployment].Requery
   [Forms]![frmPerson]![sfrmAgency].Requery

But, my guess is sfrmEmployment and sfrmAgency are not the names of subform
controls on frmPerson, but the names of the forms being used as a subform.

This version is closer, but again I think you are using the name of the forms.

   [Forms]![frmPerson].[sfrmEmployment].[Form].Requery
   [Forms]![frmPerson].[sfrmAgency].[Form].Requery

The correct refernce is to use the name of the subform control, not the name
of the form.  The main form knows nothing about the forms being used as
subforms.  It only knows about the subform controls.  A subform control has a
Source Object property.  That is what defines the form to use as the subform.
Then you have to use the Form reference because it is what identifies the
refence to the form being used as a subform.  So, the short of it is, change
the names to use the control name, not the form name.  If the subform is on
the main form where your code is, all you need is:

   Me.SubFormControlName.Form.Requery