Change it from an Array to a List of strings, then use the Add method to include another string in the list. At the moment, you load each line into the same array element, which means you end up with just the last value.
Dim r As StreamReader = New StreamReader(strFilePath)
Dim lines As New List(Of String)()
Dim intLine As Integer = 0
While (r.ReadLine() IsNot Nothing)
rowLength = rowLength + 1
eachLine = r.ReadLine()
If (eachLine.Contains("Connection reset")) Then
lines.Add(eachLine)
intLine = intLine + 1
MsgBox("Exception Found at Row = " & rowLength)
End If
End While
If you really need the list as an array at the end, you can use the ToArray method.