Problem solved !
In fact it was an issue with struts. When files were small enough to be transfered before the first call to the uploadHandler script, struts already took its hands on the file. Therefore parseRequest returned an empty list because struts did already take care of the file. Disabling that struts behavior solved the issue with small files.
Thanks for your time Fedor and sorry to have bothered you with a non-dhtmlx related problem.