You were right to suggest looking at the App Pool resources and the Event Viewer on our server.  We have  "A worker process with process id of 'xxxx' serving application pool 'xxx' has requested a recycle because it reached its virtual memory limit."  So our application pool has a hard limit on the virtual memory that was deliberately set low to force recycling.  It was set low to force recycling since a program we need to use had some "undocumented feature" that it does not count the number of users using it correctly, so someone found that recycling the pool more often would allow the program to keep working.  There is some resistance to increase the virtual memory since they do not want that program possibly crashing again.  Or we may have to switch how we are using that other program to prevent this frequent cycling.  Whatever, that is stuff we are going to have to work out.

I disabled the Site Crawler job for now, and see how things go.  See if that is enough to get rid of this "LuceneController is disposed and cannot be used" error.  Just to be clear, that Site Crawler job is only used when users are attempting to search through the site correct?