When you move a node, eZ Find does not update the index for it's underlying subtree.
The actual node is updated, but not it's subtree.

The existing documentation does not list this case under 'Important Note':
http://doc.ez.no/Extensions/eZ-Publish-extensions/eZ-Find/eZ-Find-LS-5.0.0/Basic-Configuration/Updating-the-search-index

Notes:

This can be resolved by:

• using DelayedIndexing, or
• executing the bin/php/updatesearchindex.php script