RECURRENT CURL TO A VIRTUAL SERVER FAILING

I'm not sure there is enough information to exactly resolve your question, but the BigIP will accept multiple connections from the same IP even if it has not finished the three way handshake on previous connections from the same IP. If you generate enough connections, you may trigger AFM, DoS protection, or SYN cookies, however. This would be a lot of connections, probably far more than you would create with a manual curl.

Secondly, you wouldn't care about the PuTTY connections (port 22 or 23) in the capture, you'd be looking for the curl connections (port 80 or 443). The spurious retransmissions may or may not be relevant. If you are having dropped packets on your BigIP a support case is likely to be your fastest route to resolution.