SSAS queries time out when Windows File System Cache drops
I believe you seeing the symptoms of an issue with Windows 2003 requiring contiguous memory and this causes the running processes including Analysis Service to trim their Working Set memory.  With large amounts of memory allocated this trim process can take a significant amount of time to complete, while this is running new allocations will be blocked, causing the process to stall.
This issue is fixed in Windows 2008 onwards this support article is for SQL Server but has all the links to the relevant pages http://support.microsoft.com/kb/918483 in particular this quote


  In Windows Server 2008, the allocation of physically contiguous memory
  is greatly enhanced. Requests to allocate contiguous memory are much
  more likely to succeed because the memory manager now dynamically
  replaces pages, typically without trimming the working set or
  performing I/O operations. In addition, many more types of pages—such
  as kernel stacks and file system metadata pages, among others—are now
  candidates for replacement. Consequently, more contiguous memory is
  generally available at any given time. In addition, the cost to obtain
  such allocations is greatly reduced.


I believe that with this issue you will either have to upgrade to Windows 2008 onwards or test granting Lock Pages In Memory to the Analysis Services account.  I have also had issues with memory allocation on Windows 2003 which requires a reboot to clear.

This SQLCAT blog compares the changes between Windows Server 2003 &amp; 2008.

This blog mentions some of the issues of LPIM with Analysis Services (near the end)

Also this knowledge base article on working set trimming causing performance problems and this article shows how to Identifying Drivers That Allocate Contiguous Memory