Your question is unclear if it doesn't work at all, or if it stops working after a while (and then how long ?)
I suppose your F5 VS (Virtual Server) is of type Standard.
First, we can check if the HTTP Profile is in any way guilty. If your Virtual Server type is Standard virtual server with Layer 7 functionality, change it if possible to Standard by removing the HTTP Profile (and maybe some other profiles, such as caching..). You also can try Performance Layer4 type. Is it solving the issue ? If yes, we need to identify where the problem is, probably in the HTTP Profile or in a timeout setting as described below.
Check the HTTP Profile configured for your VS, at the Response Chunking option and set it to Preserve. See LTM HTTP Profile Option: Response Chunking if you need more details.
Check both Server and Client TCP Profiles related to your VS, their Time Wait option should be Indefinite if you suspect a timeout issue. There are other ways to solve a timeout, I'm just giving one of them. See K70025261 if you need more details.
As you're running SSE, you should probably disable Delayed Acks (enabled by default) and Nagle's Algorithm (disabled by default), as they can make your notifications slower. They're also both at the TCP Profile screen.