It kind of sounds like you have an undisposed resource somewhere that ends up getting garbage collected eventually, but not quickly enough for your needs. Do you reuse any SQLConnection objects? Or MailClient objects? Or unmanaged Image objects?
As for the lower-than-expected memory limit, there are two types of memory use by a ASP.NET app. One is reserved memory and the other is actually used memory. I believe the task manager tracks actual memory use, but reserved memory probably also has a limit. To find out how much reserved memory your process is taking up, go to IIS7, click on the server (the top level, above app pools and sites folder), then click the Processes option and then click your app's process. It should show you CPU use, number of requests and memory usage (both reserved and actual).