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Why do I get logged out of LastPass when I close my browser despite my preferences?
Even if your LastPass preferences are set to keep you logged in when you close your browser, some programs and extensions, like HTTPS Everywhere, can negate these settings. You may need to test and see what is affecting this behavior by temporarily disabling some of your other extensions. Extensions like NoScript have also been known to cause problems, it's important to test LastPass without extensions active.
If you cannot figure out what might be causing the problematic behavior, contact LastPass support.