I finally found a solution.
Browser do not allow too many connections to a domain at the same time. For firefox and chrome, the limit is 6.
One of the solution, is to use subdomain. To do that, you need to add an entry for *.mydomain.tld on the DNS. On the PHP script you need to add
header('Access-Control-Allow-Origin: *');
to allow requests from others domains.
And finaly, in you JS application, you need to create a random subdomain (Math.random) and use it in all your Ajax call.