First, go to Start > Control Panel > System and Security > Windows Firewall > Allow a program through Windows Firewall and check the box next to The Sims 3. If you can't find the game in the Allowed programs and features window, press the Allow another program button, navigate to the installation directory, select the executable file and press Add.
After that, from the Advanced Settings select Inbound Rules > New Rule. Check the Port box, click Next, select All local Ports and follow the self-explained steps. Also, make sure that your security program doesn't block the connection.
If the problem persists, download and install the latest version of Origin from the official web page and reinstall the game. Origin is the new download manager developed by Electronic Arts. It replaced EA Download Manager and it is compatible with Windows XP, Windows Vista, Windows 7 and Mac OS X platforms.