Well, how many visitors does your site get? There is a connection limit of 200 simultaneous visitors/connections for websites. Maybe you're website is getting too many visitors? It has been reported that DH sometimes raises the limit if you talk to them.
Promo-Code: [color=#CC0000]SAVEMONEY97[/color] - Save [color=#CC0000]$50[/color] on your first year of hosting.
Get more promo codes here