[Rhudi]

[SOLVED]

Here is the relevant section that now works as expected:

Select Case bConnected
    Case True ' Connected
        UserName = env("USERNAME")
        UserProf = env("USERPROFILE")
        objTab.Caption = strConnectType & strShortHostName
        objTab.Session.SetStatusText("Connected: " & strConnectType & strShortHostName)
        Call CLS
        objTab.Session.Log False
        objTab.Session.Config.SetOption "Custom Log Message Each Line", "%h:%m:%s | "
        objTab.Session.LogFileName =  UserProf & "\SecureCRT Logs\" & UserName & "\%Y-%M-%D.%h.%m - " & strShortHostName & " -- (" & UserName & ").log"
        objTab.Session.LogUsingSessionOptions
    Case False ' Not Connected
        crt.Dialog.MessageBox "Try again later:" & vbCrLf & strShortHostName
End Select

This is what fixed it:

objTab.Session.LogUsingSessionOptions