Connection Lost error

We have a site hosted on 123eHost.com and lately we on WP 4.0 as well as WP 4.1 we have been experiencing extreme slowness to the website and getting the error:

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

This is a WishList Membership website running on a Genesis Theme by StudioPress

I cannot do the usual testing like deactivating the plugins or switching out a WP theme as this is a very widely used membership LIVE website.

I am sure the issue is related to the hosting server. But not sure what to tell them to look at to fix any settings.

When we ran on WP 3.9, never had this issue. Also this hosting server has several other WP websites for this same client that all function perfectly fine with no error happening. It is a private account, not shared.

Any Suggestions would be greatly appreciated.