Are you using Origin in Game or OBS or Xsplit or FFsplit or Shadowplay or Raptr/Gaming Evolved?
I assume Origin in Game?
Make sure you don't have any other overlay programs running. Origin in Game hates other overlays.
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Close any unneeded programs.
Clean Boot
http://support.microsoft.com/kb/929135
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Disable Firewall/Antivirus programs to test.. if that fixes re-enable and add exception rules.
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I am not a streamer. I couldn't find an issue quite like what you describe on google.. could only find a few OiG Twitch streamer problems (mostly involving freezing).
If you can't get it... I'd suggest looking for an alternative way to stream. If you do go that route, I'd probably turn Origin in Game off.. I don't think it's needed for any function in Sims4 that is important but I may be wrong. I am not familiar with Sims4 either that much.
*edit*
Flush your DNS cache
ipconfig /flushdns
If you are determined to use OiG to stream.. maybe uninstall Origin and reinstall. This does not remove data in \Origin Games\ folder.
