Okay… so just as I was completing this question I figured out the cause.
Using Firebug (in Firefox) I would see a lot of errors regarding access to svg and woff and ttf files under /wp-content/ was blocked. Errors like:
"NetworkError: 403 Forbidden - https://www.domainname.com/wp-content/plugins/sg-cachepress/css/logo-white.svg"
"NetworkError: 403 Forbidden - https://www.domainname.com/wp-content/themes/genesis/lib/css/fonts/genesis-icon.woff"
Seeing this, I realised when we recently hardened up the security of this site, there was code added to the .htaccess in /wp-content/ as follows:
Deny from all
<Files ~ ".(xml|css|jpe?g|png|gif|js)$">
Allow from all
</Files>````
The file types (that access to is allowed) does not include those used for the icons.
I have modified this line to include the missing file types:
`<Files ~ ".(xml|css|jpe?g|png|gif|js|svg|woff|ttf)$">`
Problem solved.
I am posting a record of this just in case it helps someone else who follows similar steps (recommended on numerous sites and blogs) for hardening security, and ends up with lost icons, etc.