But if I try to download the PCAP file I get the download dialog and an error "pcap from ASA-IP could not be downloaded". I have packets in my capture so there should be a PCAP file.
In order to download .pcap file you can use both CLI and Web Browser.
From CLI just copy the *.pcap file to a TFTP server
ASA#copy /pcap capture:cap_name tftp://tftp_ip_add
From web browser just add "/pcap" comment end of the "https://ip_add/capture/test/pcap" url.
I hope it will work fine.