A private conversation between a Facebook user and your Facebook business page does not create a ticket or an individual reply from the end-user or Facebook page administrator, outside of Support, is not appearing in the Support ticket.
If the messages for certain conversations are not creating tickets in Support but others are working as expected, the user likely has disabled access by 3rd-party apps as discussed in this article.
Individual Replies Missing
Alternatively, if individual replies are not showing, the conversation was likely archived on Facebook.
To continue conversations with users who have disabled access by 3rd-party apps, a Facebook page admin will likely have to reply to the user directly on Facebook. If the user changes their Facebook permissions in the future, messages after that point should pull in successfully.
Encourage Facebook page administrators to not archive conversations so quickly. The replies should pull over in a matter of minutes, but archiving a conversation immediately after a reply can cause for the comments to not arrive in the Support ticket.