Hey John,
If you’re running stock WordPress 3.8, and default theme, this is probably going to be something on your hosting provider’s end. It could be that the server is overloaded, or possibly your account is being throttled with something like CloudLinux.
Are you on a cPanel based platform? If you login to your hosting control panel, are there any metrics on if your site is hitting limits or bottlenecks?
I definitely recommend you open a ticket with your provider.
Thanks!
Bobby
InveHosting.com