WP and website become inaccessible after edit

I’m having an issue in which WordPress is becoming unresponsive and my website unavailable. I’ll try to make it clear what’s happening. It seems as if I take too long with a post, I’ll get the following error:

Connection lost. Saving has been disabled until you’re reconnected. We’re backing up this post in your browser, just in case.

At that point, however, I’ll get stuck with an infinitely rotating loading circle and the page will become completely unresponsive. If I try refreshing, nothing happens. Once this occurs, I am also unable to access the website itself. I am able to temporarily fix this issue by clearing the cache, but it happens within a couple minutes. The issue appears on both Safari and Chrome, so it does not appear to be browser-specific. I don’t know if it is chance, but I have not seen the issue until v4.0. I would greatly appreciate any help!