Webmail Connection Troubleshooting

My husband has a Macbook Pro running OS 10.11.6. He has trouble logging on to his work webmail (his school at state university server) through our home internet. Sometimes it connects all right, sometimes it times out (TLS handshake, per Firefox status bar. Also happens on Safari.).When he does connect, it can hang on displaying a selected message.

This doesn’t happen on any other devices (iMac, iPad) here.
This doesn’t happen anywhere else (airport, daughter’s house) but here.
This doesn’t happen with any other websites.

Where do I look for the problem? Any clues as to what it might be or what might solve it would be great, thanks.