As it stands at the time of this post, Xbox live is having problems with game invites and party invites. Microsoft is aware and working on the issues. For more information go to: http://support.xbox.com/en-US/xbox-live-status
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They claim it's fixed but it's still not working
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At least I know it's being looked in to now.
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I'm glad they're looking into it, but they need to make sure this doesn't happen.
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Thanks for the heads up!