Hi Andy,
Owing to Internet security issues last year (Heartbleed, etc), most web servers only allow TLS 1.2 connections. It's a newer negotiation and encryption protocol than SSL 2 or 3. I do not believe any Amiga TCP stack supports it.
My workaround is to use the NetSurf browser because it implements its' own security. It's definitely not as quick or stable as IBrowse or AWeb, and it's pretty resource-hungry. Sites look and work much better with it because of the CSS support.