There are some situations when some contacts cannot be blocked (for example, if they have permissions to broadcast messages).  The mobile app is not handling this situation correctly, and it gives the false impression that a user was blocked.

The endpoint to block users is core_message_block_user and doesn't give an indication that something went wrong. However, it is possible to use the information in a call to core_message_get_conversation looking at the canmessageevenifblocked property of the user.