Hi,
It sounds pretty logical that a static HTML website is going to be more reliable than an ASP .NET based one, simply because the dynamic site is using far more resources when pages are accessed.
If an ASP .NET website encounters a problem, though, it has the capability to restart, or "recycle" itself. To be honest, almost all web applications I have ever seen need to be recycled periodically, because they hold onto sessions for too long or just plain fragment the memory space too badly. The IIS 6 Administrator snap-in has recycling settings under the "application pools" container that can be used to configure what will trigger recycling, whether it's high memory usage, a certain time, or after a certain number of requests.
If there is a serious problem that causes the application pool to recycle repeatedly in rapid succession, then "Rapid Fail Protection" may have kicked in and permanently disabled the website. This is configured on the Health tab of the application pool properties page.
Most times, there is an adequate explanation in the System log that will say why the IIS process had failed. It may be something easily fixed administratively, for instance by adding more memory to the server or reconfiguring some services.
In serious crashes where the website's code may be to blame, it may be useful to try Microsoft's DebugDiag tool to figure out what had happened.
I hope this helps!