Hi Johannes,
I highly doubt that your F5 will resend the ongoing HTTP request to your pool members. Its more likely that the F5 ends an idle TCP connection (e.g. Idle Timeout of the default tcp profile is 300 seconds), and the browser automatically sends a retry in the background.
You could try slightly longer "Idle Timeouts" (recommended) or alternatively use "Keep Alive Interval" settings with a value lower than "Idle Timeouts" setting (use this with caution, it will keep the connection alive as long as the client is reachable).
Cheers, Kai