I dont think your problem has got anything to do with multi-threaded web applications BUT rather by the solution architeture itself

It could be your server is not configured properly to handle the bandwidth or just your application has a memory leak somewhere.

Make sure you close all connections EXPLICITLY especially if you are using a dataReader object and try again.

An access mdb file can handle up to 20 concurrent users altho many ppl will dispute that but I am sure it can handle 2-5 users