Because this is an intermittent problem the first thing I would do is make sure that I have a fresh start on the server. An intermittent problem can mean that most of the child processes serving web requests are working fine, but one of them is not and it causes errors whenever it is chosen to handle the request.
So turn off the apache server and use "top" or "ps" to check the processes and make sure that all the httpd processes have stopped. You might have to kill some of them manually if they refuse to stop.
Then restart the server and whether these errors reoccur. In general the errors sound like difficulties with the server software, perhaps a child with a memory leak, rather than webwork specifically. If Parser.pm were really not available you would get that message every time.
Hope this helps. Let us know how things turn out.