There was a post several years ago with the same issue. Is setting this header in IIS still disabled due to being in a shared environment? If so, is there any upgrade or plan (I'm currently on Max) that would allow it? Note: I am not interested in "keeping my site alive" (i.e. constantly pinging it / using resources to prevent a cold start). This is strictly about the HTTP header. It's kind of a deal-breaker and I would pay good money to have this option.
Contact our support department and ask them to enable HTTP Keep Alive. We will provide more details on the ticket. support.winhost.com