Based upon your syntax, it is looking for a file called objFile.Name instead of treating this as a variable. Try modifying your code to:
dim filesys
set filesys=CreateObject("Scripting.FileSystemObject")
Set objFSO = CreateObject("Scripting.FileSystemObject")
Dim objShell
set objShell = CreateObject("WScript.Shell")
strSearchFor = "Login Failed"
Set oFSO = CreateObject("Scripting.FileSystemObject")
objStartFolder = "C:\TelnetLogs\Query1"
Set objFolder = objFSO.GetFolder(objStartFolder)
Set colFiles = objFolder.Files
For Each objFile in colFiles
strFile = "C:\TelnetLogs\Query1\" & objFile.Name
set objFile = objFSO.getFile(strFile)
if objFile.size > 0 then
If InStr(oFSO.OpenTextFile(strFile).ReadAll, strSearchFor) > 0 Then
filesys.CopyFile "c:\TelnetLogs\Query1\" & objFile.Name, "c:\TelnetLogs\Failures\" & objFile.Name
Else
WScript.Sleep (100)
END If
END If
Next