Some other interesting information :
When we try to run the program, using another Provider Services (running on another server), and connecting to the same Essbase server where we had the network error, it works fine. This means that there is a specific problem with the Provider services server that is used. But I'd like to find out what is this APS problem.
And to complete the previous response, the problem is the same running the java program directly on the problematic server, or on a remote Windows laptop...