이러면 어떨까요!

다른 쪽 서버쪽에 Ping을 쏴서 안가면 에러처리를 하시면 될 듯 하군요!

델파이 컴포넌트 있는 ICMP 컴포넌트를 사용해 보세요
var
PingList : String;

procedure TForm1.ICMPReply(ASender: TComponent;
  const ReplyStatus: TReplyStatus);
var
  sTime: string;
begin
  If (ReplyStatus.MsRoundTripTime = 0) then
  sTime := '<1'
  Else
  sTime := '=';
  PingList := Format('%d ',[ReplyStatus.BytesReceived]);
end;

procedure TForm1.Timer1Timer(Sender: TObject);
var
  k: integer;
  ping1 : String;
begin
  ICMP.OnReply := ICMPReply;
  ICMP.ReceiveTimeout := 500;
  ping1 := '192.1.1.1';

  try
  ICMP.Host := ping1;
  For k := 1 To 2 Do
  Begin
  ICMP.Ping;
  Application.ProcessMessages;
  End;
  Except
  Begin
  ICMP.Ping;
  Application.ProcessMessages;
  End;
  End;

  If Copy(PingList,1,1) <> '0' Then
  Begin
    DM.Form_DBS.Connected := True;
    Edit1.Text := '접속가능';
    Edit1.Font.Color := Clblue;
  End
  Else
  Begin
    DM.Form_DBS.Connected := False;
    Edit1.Text := '접속불능';
    Edit1.Font.Color := ClRed;
  End;
end;

procedure TForm1.ICMPReply(ASender: TComponent;
  const ReplyStatus: TReplyStatus);
var
  sTime: string;
begin
  If (ReplyStatus.MsRoundTripTime = 0) then
  sTime := '<1'
  Else
  sTime := '=';
  PingList := Format('%d ',[ReplyStatus.BytesReceived]);
end;