"Connection lost" problem won't go away

Hi, recently I began seeing the “Connection lost. Saving has been disabled until you’re reconnected. We’re backing up this post in your browser, just in case.” error pop up repeatedly in one of my WordPress sites.

I have looked around and tried the remedies I could find in other forum threads: I have deactivated all plug-ins. I’ve switched to the default theme. I’ve flushed my browser cache (I don’t have any caching set up in WordPress). I have lengthened the AutoSave interval. This morning I manually upgraded to WordPress 3.7.

Still getting the error message.

I have also checked with my web host; they don’t report any problems. (And they aren’t GoDaddy fwiw.) And in fact I have another WordPress site hosted in the same place, and it seems to be working fine without the Connection lost message.

Any ideas…? Please let me know what other information I can provide. Thanks so much for any thoughts that may help!