This is usually caused by either server firewall problems, or using incorrect login crendentials particularly leading or trailing spaces when using copy and paste.
You can display a dump of the comms I/O using the debug options packgaed with StageShow. In the stageshow/admin folder rename the stageshow_xdebug.php file to stageshow_debug.php. No go to the StageShow->DEBUG admin page, select "Show PayPal IO" and then "Save Debug Settings". Now retry the login. The response will give you an indication of the response to the login request. Unselect the "Show PayPal IO" option and save when you have finished testing.
If you are still having problems, contact me with the results of this test via my website, and I'll try to help.