I recently setup an index password protected posts on my WordPress website. All of the posts in a particular category needed to be password protected, but also searchable to non-logged in users.
The default WordPress search box will not index and serve password protected posts in search results unless you are logged in.
In just a few minutes I was able to find a solution so I figured I'd share. This awesome WordPress plugin and solution is called "Relevanssi" - download the plugin here: http://wordpress.org/extend/plugins/relevanssi/
Relevanssi replaces the standard WordPress search with a better search engine, with lots of features and configurable options. You'll get better results, better presentation of results - your users will thank you.
The plugin has been downloaded well over 180,000 times so we can infer this a pretty solid solution to lots of WordPress users.
The WordPress community has always been reliable to fix almost any problem I've ever encountered when building a website. Compared to some other issues I've experienced, this was one of the quickest solutions I've ever found. In fact, once I installed Relevanssi, the password protected posts immediately showed up in search results. This plugin has extensive customization capabilities that will surely play in a role in all my future development projects.
If this plugin helps you out, as always, please consider donating to the authors or purchasing the premium version - which likely has some other great features to help you.