The search results for your website are done by your theme not the WordPress core. I think the theme may be conflicting with a plugin or the WordPress core.
Try contacting your theme developer in there WordPress support forum. Also try deactivating all plugins. If that resolves the issue, reactivate each one individually until you find the cause.
WordPress theme Responsive support forum:
https://wordpress.org/support/theme/responsive
I expect the change is deliberate and is to do with accessibility standards, ie a title should be a title not a link.