The ProxySG will only split live streams under the following conditions:

The ProxySG can only split streams for clients that request the same stream.

First, the client connects to the ProxySG, which then connects to the origin server and requests the live stream.

Subsequent requests of the same content from different clients are split from the appliance.

Two streams are considered identical by the ProxySG if they share the
following characteristics:

• The stream is a live or broadcast stream.
• The URL of the stream requested by client is identical.
• MMS (Microsoft Media Services), MMSU (MMS UDP), and MMST (MMS TCP) are considered to be identical.
• Native supported streaming protocol must be used by the client to communicate with the proxy SG, i.e. MMS, RTSP, RTSP over HTTP.

If it's the latter, then HTTP handoff must be enabled.