Cool possibilities here. I found some things:
1. intReadyState has to be reset for each web  site
2. wait an additional 1 sec after intReadyState = 4
3. use LCase to make it not case sensitive


Sub Main()
Dim objIE As Object
Dim strWebSite As String
Dim intReadyState As Integer
Dim order  As String
Dim n, a, total  As Integer
n = 1
total = Worksheets("sheet1").UsedRange.Rows.Count
Set objIE = CreateObject("InternetExplorer.Application")
While n <= total
strWebSite = Worksheets("sheet1").Range("a" & n).Value
objIE.Visible = 1
objIE.Navigate strWebSite
intReadyState = 0
Do While Not intReadyState = 4
intReadyState = objIE.ReadyState
Loop
'wait an additional 1 second
PauseTime = 1 'seconds
Start = Timer
Do While Timer < Start + PauseTime
DoEvents ' Yield to other processes.
Loop

DocText = objIE.Document.body.innerhtml
DocText = LCase(DocText)
'Call SaveDoc(DocText, "DocText" & n & ".txt")
If InStr(DocText, "mail") = 0 Then
Worksheets("sheet1").Range("b" & n).Value = "not
exists"
Else
Worksheets("sheet1").Range("b" & n).Value = "exists"
End If
n = n + 1
Wend
Set objIE = Nothing
End Sub

Sub SaveDoc(TheDoc, fName)
Path = Application.ThisWorkbook.Path & "\" & fName
fn = FreeFile()
Open Path For Output As fn
Print #fn, TheDoc;
Close #fn
End Sub

Really those are the cool possibilities. Its working  very much fine  now, with
appropriate result. Thanks a lot for this support.

How about this variation of what you have:

Dim objIE As Object
Set objIE = CreateObject("InternetExplorer.Application")
sFind = "mail"
For Each oCell In Range("A:A")
If oCell.Value = "" Then Exit For
With objIE
.Navigate oCell.Value
Do Until Not .Busy
DoEvents
Loop
sData = .Document.documentElement.innerHTML
End With
If InStr(sData, sFind) > 0 Then
oCell.Offset(0, 1) = """" & sFind & """ was found!"
Else
oCell.Offset(0, 1) = """" & sFind & """ not found!"
End If
Next oCell
objIE.Quit
Set objIE = Nothing