There are so many tools you can use, but wget makes it simple:
$ wget -m ftp://site.tld/folder/
And If you need authentication:
$ wget -m ftp://host.tld/folder/ --user=username --password=password
There are tools that will let you do batch downloads, but wget works sequentially on one file at a time. I think that’s a reasonable balance between getting the material and respecting the target site’s bandwidth.
As I said on that show, I’m realising that if you treasure something online, you need to preserve it yourself. Or if you’re allowed to, send it to the Internet Archive.