Hi,
I am facing same 'Login Rate Exceeded issue'. Would really appreciate your help on fixing this. I am new to SalesForce and first time doing this integration. I call the 'getConnection' method each time before making API call. Inside that method I check if connection is not null then I return the same connection object or else I create a new one.
I am not sure why I get this error. The method code is like below.

private EnterpriseConnection getConnection(boolean loginRequired){
		//get all the related properties
		
		String userName = sfdcProps.getProperty("sfdc.username");
		String password = sfdcProps.getProperty("sfdc.password");
			
		logger.warn(" \n\nloginRequired " + loginRequired +" UserName = " +userName + " pwd = " +password );
		
		if(connection != null && !loginRequired) {
			return connection;
		}
		else{
				try {
					 ConnectorConfig config = new ConnectorConfig();
					 config.setUsername(userName);
					 config.setPassword(password);
				 	 //config.setTraceMessage(true);
				 	 //config.setPrettyPrintXml(true);
				     connection = Connector.newConnection(config);
				     if(loginRequired){
				    	 synchronized(connection){
							 LoginResult loginResult = connection.login(userName, password);
							 String sessionId = loginResult.getSessionId(); 
							 String serverUrl = loginResult.getServerUrl();
							 connection.getConfig().setServiceEndpoint(serverUrl);
							 connection.getSessionHeader().setSessionId(sessionId);
				    	 }
				     }
					 String authEndPoint = config.getAuthEndpoint();
				      // display current settings
				      logger.info("SessionId: " + connection.getSessionHeader().getSessionId());
				      logger.info("Auth EndPoint: "+ authEndPoint );
				      logger.info("Service EndPoint: "+ connection.getConfig().getServiceEndpoint());
				      logger.info("Username: "+config.getUsername());
				    }catch (ConnectionException e1) {
					    logger.error("Could not connect to SalesForce: " + e1.getMessage());
				    }
		}
	    return connection;
	}

 PLease help.

Thnaks,

mk2013