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I wrote a blog post with detailed instructions how to get both local and remote parts working, took me some time to get everything figured out: http://danieldemmel.me/blog/2012/09/02/setting-up-rmate-with-sublime-text-for-remote-file-editing-over-ssh/

For me the culprit was the Modific package (similar to what Alexander posted), this user setting solved it:

{

    "autosave": false

}