It's well known that the Page speed affects the rankings so yeah there's no reason for Google to show up a offline url on top of the search results. It definitely affects the rankings but also depends on how long your site is down and how much authority it has got. Better fix your downtime or move your site's to much stable hosting providers.
Okay once RMX comes back online I am going to go about sortint out a new reliable host for my websites
Also, once I get my site on the new host with full uptime will I see my rankings come back again? I sure hope my SEO work is not lost