The information doesn't disappear as such; it'll still be there when you go back to the slide where you originally entered it. It just won't automatically appear in an ActiveX text box on other slides.
The text box's Lost Focus event will fire when you move from one slide to the next, so some code in the Lost Focus event could look at each slide in the presentation, accumulate any text in any text box control, then make the text in each text box match the accumulated text.
This isn't perfect but if you want to have a go at it, it's a start. Apply this code to the LostFocus event of each control. For more help with it, post questions to StackOverflow with Powerpoint and VBA tags rather than here:
Private Sub TextBox1_LostFocus()
Dim oSl As Slide
Dim oSh As Shape
Dim sText As String
On Error Resume Next
' Accumulate text from all ActiveX text boxes
For Each oSl In ActivePresentation.Slides
For Each oSh In oSl.Shapes
If oSh.Type = msoOLEControlObject Then
sText = sText & oSh.OLEFormat.Object.Text
End If
Next
Next
' Apply the accumulated text
For Each oSl In ActivePresentation.Slides
For Each oSh In oSl.Shapes
If oSh.Type = msoOLEControlObject Then
oSh.OLEFormat.Object.Text = sText
End If
Next
Next
End Sub