Hi,

yes there is a limitation; a limit is posed by browsers on the number of concurrent connections open to a certain server.
Actually the http protocol dictates a maximum of 2 concurrent persistent connections per client(browser)/server but most browsers permit more connections.
[You can act on this limit on firefox by changing the network.http.max-persistent-connections-per-server setting in the about:config page]

You should be able to work-around this limit by using different host names in each flex application instance or by letting only one flex application connect to the server and connecting the others to the first one using Flex's LocalConnection class.

HTH