Users have complained for months that Public Folder Favorites were not being cached in Outlook 2016, even though caching Public Folder Favorites was enabled in Account Settings, More Settings.
This also affected the ability to search public folders: because the items weren't cached, Outlook wasn't indexing the folder contents. Search only worked if you unchecked the Download shared folders option which switched the folders to online mode, where items were indexed by the server. This also made large public folders slow to use as the contents needs to sync down every time you switched to the folder.
This issue was fixed in the in the January 3, 2017, update for Outlook 2016 (KB3141453) for MSI installations. Users with the Click to Run installations (most people) will see the fix soon, if not already.