Delay between two HTTP requests in a common TCP.flow (between 10 - 30 seconds)

In the packet capture that you did on the F5, are you seeing duplicate ACK's or re-transmission requests?

You did a capture on the server, the F5, and the client. But I don't see where you did any captures on the devices between the F5 and the client.

If you can see the packet leaving the F5, and NOT arriving at the client, then it is getting dropped someplace in between.

You would need to do packet captures at various points to see where the packets are getting dropped.

I doubt that the LTM3900 itself is having a problem, my guess is that someplace in the network between the 3900 and the clients is having a problem.

You say the 3900 has 2 connection setup in LACP. Are both connections to the same switch or are they to 2 different switches?

If to the same switch are both switch ports configured in a LACP group?

If different switches, do both switches have clean paths to the client?