I cannot give an answer to that because there are just too many reasons for causing this. I hope your specific question and/or use case is within the next part.

Do you have permissions to access content and view user profile?

Note that heartbeat does not know about links being used in the messages. For this reason heartbeat set the choice to show these messages OFF by default. So you have two options here:1) Enable the setting, allowing all messages showing links (or not even using links at all) and have a small problem with the access denied page, or 2) Leaving it disabled and never show messages that have a node or user within the context of the message. Together with this setting you should enable the drupal permissions "access user profile" and "access content" for that matter. Since this is the default setting i prefer doing things this way. The decision is based on the fact that this is a community module and users should see content and user profiles.

Is the database correctly filled?

You can always check the database table heartbeat_activity to see if your message was logged. The message field should be a proper already built and well-formed message.

Recheck the access on the messages

Check if the messages are not blocked by message type role permissionCheck if the messages are not blocked by the user disabling that message typeCheck if the stream allows that mesage typeCheck if no filter is blocking the message from stream