Log in twice via Idhttp - delphi-7

Question

I have placed an Idhttp component on my main form and an IdSSLIOHandlerSocketOpenSSL and both components are not adjusted via the IDE. I use it to access two servers:
1) A http server which requires an authentication;
2) A https-server (which requires an authentication).
When I connect via Idhttp to server (1) I can connect via a regular fashion. However, when I connect to server (2) it returns a message that the user credentials are not correct.
I tried switching the procedures but then I cannot login into server (1): I get in both situations the response from the server that I input wrong credentials.
I presume some property is changed. I checked the Idhttp.Request.UserName and Idhttp.Request.Password before I connect and they are correct.
What is going wrong?
procedure TForm1.AccessServer1;
var
fs: TMemoryStream
begin
fs := TMemoryStream.Create;
IdHTTP1.Request.BasicAuthentication := true;
IdHTTP1.Request.UserName := myUsername1;
IdHTTP1.Request.Password := MyPassword1;
try
IdHTTP1.Get(myURL1, fs);
fs.SaveToFile(MyFilename);
finally
fs.free
end;
end;
procedure TForm1.AccessServer2;
var
fs: TMemoryStream
begin
fs := TMemoryStream.Create;
IdHTTP1.Request.BasicAuthentication := true;
IdHTTP1.Request.UserName := myUsername2;
IdHTTP1.Request.Password := MyPassword2;
IdHTTP1.HandleRedirects := True;
IdHTTP1.IOHandler := AIdSSLIOHandlerSocketOpenSSL;
try
IdHTTP1.Get(myURL2, fs);
fs.SaveToFile(MyFilename);
finally
fs.free
end;
end;