You fail to initialize intC
before starting the while
loop, and you're not incrementing it within the loop, so it never changes to exit it (presuming it gets inside the loop in the first place), which would make it seem to "lock up".
Set it to a starting value first, before you use it.
Private Sub btnSave_Click(sender As Object, e As EventArgs) Handles btnSave.Click
Dim outFile As IO.StreamWriter
Dim intC As Integer = 0
outFile = IO.File.AppendText("persons.txt")
Do While intC < count
outFile.WriteLine(peopleDescription(intC))
intC += 1
Loop
outFile.Close()
End Sub