we did this and it worked great. we set tcp_keepidle on AIX to 4.5 minutes and the BIGIP was happy to keep the connection open. We also found that the connection was kept open from the Windows PC to the BIGIP. That was a surprise. Is that because the BIGIP is sending the heartbeat ALL THE WAY back to the PC??
So we have PC->BIGIP->WEB and we set the tcp_keepidle on the WEB AIX box ONLY and it seemed to work fine. So we assumed the BIGIP sent the heartbeat all the way back to the PC to keep that connection open.
Make sense?