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This is pretty hard to give a good answer to without knowing the site, but a significant sudden drop is usually not tied to smaller factors like page speed. Rather, they tend to be tied to low quality link building (penguin), low quality content (panda), over optimization penalties, or technical problems (look for noindex, robots.txt, nofollow, canonical issues). I know it's a bit broad but without a specific URL, I'd start looking there. Good luck! -Geoff