While I'm not a huge fan of simply re-posting content originating on other individual's blog, this particular re-post is warranted, if for no other reason that it was a bear to find the solution. My hope is that more references to the posting will increase the likelyhood that someone else will spend less time finding the answer in the future.
Now, effectively the problem I encountered was an "Access is Denied" message when trying to schedule a search crawl in Office SharePoint Server 2007 (RTM). While, I could manually start a crawl and it would successfully complete, I was not able to create a schedule for either an incremental or a full crawl. Apparently, the trouble was missing permissions on the Tasks folder in the Windows directory; the "WSS_WPG" group (created by SharePoint during installation) needed read and write access to the folder.
It totally makes sense that SharePoint would leverage scheduled tasks to kick off scheduled crawls, but I would have hoped that the installation process set this for you. In my case, the server I dedicated to the index function was a "recycle" and was never reloaded with the OS -- the prior implementation of SharePoint was uninstalled and I re-installed the new implementation over top. In hindsight, this may not have been such a good idea, but we live and learn.
Here's the article that saved me the trouble of rebuilding my machines (yes I was that frustrated): http://www.folin.se/index.php/category/microsoft-office-sharepoint-server-2007/
Many thanks to Michael Folin for posting such a great tip!