Just to close out this post - the user contacted Maplesoft Technical Support and some licensing issues were identified with the installation on this server. These have been addressed, and this school will resume high-volume testing with Maple T.A. 4.0. Maple T.A. installations can run from class-level sizes where a handful of students are tested at a time, to campus-wide installations where hundreds of students logon simultaneously.
One point that should be clarified - by default Maple T.A. limits the number of users that can login simultaneously to 80. This is because on some operating systems PostgreSQL cannot handle more connections than this by default. It is possible to increase the number of simultaneous users in Maple T.A. from the default of 80, but changes need to be made to Maple T.A., PostgreSQL, Tomcat, and possibly the operating system itself. If anyone runs into difficulties making these changes I would suggest contacting Maplesoft Technical Support.