IIS quits working IIS lists as running

I have an external web server that when it first fires up runs like a champ then about an hour or so later the website cannot be located. It will work again after reboot. I thought it may be a DNS error so I typed in the address instead of the site address and it still displays the normal unable to find… I am able to log on remotely so I know the connection is good. There are no errors in the event log and the IIS manager does not show any errors and it lists the site as running. Bandwidth isnot a problem either since I am able to log on remotely. I am up to date with all IIS patches. any ideas