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From the provided information we could not make a lot of suggestions for troubleshooting. Our only guess would be that you have this website running in the same application pool together with other applications. Then over time the application pool needs recycling and if the application pool keep alive interval is too long you might experience behavior as this. At this point what we could suggest you to try is to create a separate application pool for your website and set the pipeline mode, and identity of this application pool the same as the one your website is running in. Then migrate the website to the new application pool you have created, and observe the behavior.
the Telerik team