Are you talking about using HTTP 1.1 (Connection: Keepalive) with backend servers ? Take a look to the "http reuse" feature.
HTTP 1.1 persistence headers are analyzed in the incoming client request. Any connection close headers are dropped, and a connection keepalive header is added as necessary. This sets the request up to maintain the connection with the server.
Create an HTTP parameter map with "server-conn reuse" and "persistence rebalance" and apply it to your VIP.
beware, when using TCP reuse, the MSS must be the same on the back end servers and the ACE