David
Thanks for making the tracing rule available. (However, it looks like you must have enabled the tracing after URL rewrite and ARR have been installed. Did you know that URL rewrite and ARR can write more detailed information to tracing? http://learn.iis.net/page.aspx/488/using-failed-request-tracing-rules-to-troubleshoot-application-request-routing-arr/ If you do not see RequestRouting and Rewrite in the Area section, then it is probably because tracing was enabled after these modules have been installed. If that's the case, you can simply repair the two installations via add-remove programs.)
However, not having additional info doesn't really matter with this investigation.
What you have stated is exactly right. If you go to the compact view of the log, the line number 30 is where the IIS URL rewrite module has changed the URL:
OldUrl="/reports/Pages/Folder.aspx", NewUrl=http://SSRS2008/reports/Pages/Folder.aspx
And it is correctly routing the request to the serverfarm.
However, the line number 84 rewrites it to:
OldUrl="http://SSRS2008/reports/Pages/Folder.aspx", NewUrl="/UrlRouting.axd"
and then again the line number 98 rewrites it to:
OldUrl="/UrlRouting.axd", NewUrl="/reports/Pages/Folder.aspx"
Which is why it is resulting in 404.