In IIS 6, go to the Application Pools section, and right-click > Properties on the pool which hosts the ASP.NET application in question. Go to the Performance tab and uncheck "Shutdown worker processes after being idle for:"
In IIS 7, go to the Connections pane and find Application Pools, and select Advanced Settings for the pool which hosts your application. Find the "Idle Timeout" property and set it to "0" (this disables it).
The default is 20 minutes of inactivity. By unchecking the box, once your AppDomain is loaded by the worker process, it will never die (unless you kill the process or something of course). By default, IIS will recycle the process when it reaches some limit, such as a memory cap, but it will also start a new one and "phase over" all incoming requests until the old one is unused, so as to minimize disruption.
If you do not have direct control over your IIS configuration (shared host, for example) your best bet is to have a small application running on a separate system - say, an always-on workstation - which hits your site every x minutes to keep the application pool from timing out. Nothing fancy - a simple WebRequest and a while() loop in a console application will do.