You problem is caused by deleting rows top to bottom. Try the other way round instead i.e.
Dim i As Integer
For i = Range("C" & Rows.Count).End(xlUp).Row To 2 Step -1
If Cells(i, 3) = "unique" Then
Depending on how much data you have another option would be to use "Autofilter" with "unique" as criteria and then delete all the rows that matches in one go.