I was not able to download PDFs from the website with either Chrome or IE until I re-enabled SSL 3.0 and TLS 1.0. I had turned off these protocols due to vulnerabilities discovered over a year ago. See https://www.ssl.com/article/poodle-flaw-grows-bigger-tls-affected/ for background on this.
Paizo really should turn off those protocols on their servers if not because of the security risk, but because browser are dropping support for those protocols.