Why do previews work in one browser, but not another?

Question

I keep having an intermittent issue where the admin bar disappears from a wordpress site I often use, when using my main browser (Google Chrome). I can access /wp-admin/ no problem, and another problem is that post previews will not work, instead showing me the 404 page.

Safari, however, works just fine. What can I do to get Chrome to behave properly again?