For a customer we were building a news aggregation solution on Office 365.
The search would retrieve a custom content type from several sites in the current site collection and displays this on the landing page via a Content Search Web Part (CSWP).
When configuring the CSWP we couldn’t retrieve information from subsites, we received only data from the current site.
Rebuilding the content type, check permissions on subsites and many other options where tested before we opened a ticket by Microsoft.
We discovered that the customer was using E1 licenses and the CSWP is only available in E3 and E4 plans. The Webpart is available but will not retrieve any data from other subsites.
To work around you could use a Search Results Web Part, use a Content Query Webpart or upgrade the licenses.
My Customer choose for that last option.
A complete list of functions that are available in the different Office 365 plans can be found here: SharePoint feature availability across Office 365 plans