Sounds like either intermittent link connectivity issues or a dns problem, What exactly fails? Is the machine still reachable via ip? Is it just IIS on remote AD machines that are failing?
How are they tied together. Does this webserver depend on other servers or processes to be functional?
On error is there anything in the event log?
Any errors associated with this issue?
Has this setup worked in the past or are you just trying to get it going?
If it has worked in the past what has changed?
Troubleshoot, answer these questions and update! I would love to help you out,