Multiple server-side streaming calls hangs the browser

We have a web page where more than 1 grpc calls (server side streaming calls)will be made , and all these will be pending state until the server responds with one response at least.
If the number of these calls increases to 8 or 10 ,and the server doesn't send any response , subsequent normal calls are also getting blocked , making the UI unresponsive. Is there any limitation on having number of server-side streaming calls from browser