If traffic starts to slow down are you sure there is no qos applied somewhere that's restricting you from flooding the link downloading from the internet , usually traffic like that is policed for that reason stop users crippling internet links
If you really think its asp dropping the packets this may help , how to diagnose asp drops and capture them
https://www.fir3net.com/Firewalls/Cisco/what-is-asp-and-how-to-troubleshoot-asp-drops-on-an-asa.html
